Ivanka Trump and Jared Kushner are shown their seats before President Trump speaks during a working lunch with ambassadors of countries on the United Nations Security Council and their spouses on April 24. (Jabin Botsford/The Washington Post)

The president of the Czech Republic is eager to have Ivanka Trump visit his country, and he believes he has a compelling case to make.

By a “happy coincidence,” her mother is Czech, and President Milos Zeman hopes that’s the opening he needs to secure a high-profile visit from the first daughter as he tries to realize the kind of relationship with the U.S. government that his country has long craved.

“We would like her to know that we are the country where she might find a surprising number of people who will treat her very, very nice,” said Hynek Kmonicek, the Czech ambassador to the United States, who has been entrusted by Zeman to deliver a letter to Ivanka Trump at the earliest opportunity. ­“Because she’s, like, pre­approved.”

The letter remains undelivered, but Kmonicek is optimistic.

“I hope I will be able to put a selfie on the Twitter,” he said with a smile as he mused about the meeting while lounging in his Northwest Washington office.

The Czech Republic is just one of several countries that see the first daughter as an avenue of entry into her father’s White House, citing the image she has cultivated as culturally curious and active on policy as reason to think she will be receptive to their outreach. A relationship with the first daughter is coveted because she and her husband, Jared Kushner, are top White House advisers with broad, largely undefined portfolios, stretching from domestic to foreign policy, and an all-important familial connection that gives them rare influence.

(Gillian Brockell/The Washington Post)

Ivanka Trump, in turn, has used foreign nations’ interest to help soften her father’s rough edges amid uncertainty over his foreign policy and promises to upend long-standing alliances if he deems them unfair to the United States.

“She’s being seen as a goodwill ambassador slash adviser slash soft-power effort for an administration that has had a lot of challenges in those areas,” said a senior diplomat for a Latin American country, who spoke on the condition of anonymity to comment candidly about the embassies’ outreach to Trump. “By all accounts, she seems to be everything that her father is not: likable, soft-spoken, and she’s not impulsive. She seems to be thinking through everything that she does.”

As President Trump embarked Friday on his first foreign trip since taking office, Ivanka Trump accompanied him and will make public appearances on her own. She is likely to take on a similar role abroad as she has in the past four months in Washington, where she has been an enthusiastic participant in social and cultural events.

Ivanka Trump attends a reception with two of her children at the Japanese ambassador’s official residence on April 4. (Asahi Shimbun/Via Getty Images)

She and her children have made appearances at the Chinese and Japanese embassies. She visited the French ambassador’s residence and, in March, dined with the British ambassador along with Kushner.

German Chancellor Angela Merkel extended the invitation for Ivanka Trump to attend a women’s economic summit in Berlin, and Canadian Prime Minister Justin Trudeau treated her to a Broadway show with a not-so-subtle message about the virtues of taking in strangers in need.

Secretary of State Rex Tillerson, who frequently visits the White House, communicates with Kushner and Ivanka Trump regularly about diplomatic issues, including their family’s visits with embassy officials.

“One of the things that’s been useful about both Ivanka and Jared and the members of the White House staff is that they have existing relationships that they’ve built, but then they’re turning around and making them everyone else’s relationships,” said R.C. Hammond, a senior State Department adviser.

As word has gotten around the diplomatic world about the potential return on investment in courting the first daughter, embassies have begun actively looking for ways to bring her into the fold, mulling invitations to gala events and cultural celebrations where they can establish low-stakes, personal relationships with her.

Ivanka Trump, left, attends the Chinese Embassy's New Year reception with her daughter Feb. 1. (Liu Yang/Xinhua News Agency via Getty Images)

Early in her father’s tenure, Trump inserted herself into the U.S.-China relationship with a high-profile trip to the Chinese Embassy for its Lunar New Year celebration. It came at a time when President Trump was struggling to establish a diplomatic relationship with Beijing after raising the ire of the Chinese by taking a phone call from the Taiwanese president, in defiance of a long-standing “one-China policy.”

For weeks after the call from Taiwan, there was radio silence between Donald Trump and Chinese President Xi Jinping, a sign of Beijing’s coldness toward the new U.S. president. More than two weeks after Trump was inaugurated, he had still not spoken with his Chinese counterpart, despite having talked to more than a dozen other world leaders in the same time frame.

But while official diplomatic doors appeared to be closed, ­Ivanka Trump, with her ­Mandarin-speaking children in tow, appeared at the Chinese Embassy in upper Northwest Washington on Feb. 1. Doors opened, cameras flashed, and Trump smiled as she was greeted warmly by embassy personnel. The next day on Ivanka Trump’s Instagram page, 5-year-old Arabella made an appearance, singing sweetly as she played with a puppet dragon.

“Arabella singing a song she learned for #ChineseNewYear,” her mother wrote in the caption. “Wishing everyone an amazing year to come during these days of celebration.”

Days later, the freeze had thawed. In a phone conversation with the Chinese president nearly 20 days after his inauguration, Trump promised to honor the “one-China policy.”

Hammond cited President Trump’s improved relationship with China as evidence of the success of Ivanka Trump’s engagement.

“Overall, you look at the relationship that we’re building, we’re engaging with China,” he said.

At the Japanese Embassy in April, a scene similar to the one that occurred at the Chinese Embassy played out. The embassy painstakingly extended an invitation to Ivanka Trump to attend its Cherry Blossom ­Festival. Then the planning began.

Embassy staffers hatched an elaborate plan to invite Japanese YouTube star Pikotaro to perform for Arabella, who was a fan of the singer’s earworm song. They called the company that makes the video game and anime character Pikachu and ordered up stuffed dolls, and acquired other traditional Japanese toys, to entertain Trump’s young children.

The visit was a slam-dunk, in the embassy’s view, garnering media coverage in the United States and Japan, where Ivanka Trump is an increasingly popular figure.

“Ivanka plays a very important role and helps us deepen our ties and also advance strong relationships between our governments,” said Yoshinori Takazawa, a spokesman for the Japanese Embassy. “A lot of Japanese media outlets reported this event.”

As a result, “a lot of Japanese citizens believe that the U.S. and Japan are close friends,” he said.

Among world leaders, Japanese Prime Minister Shinzo Abe enjoys arguably one of the best relationships with Trump, which has been repeatedly bolstered by Abe’s efforts to connect with Trump through Ivanka and her children. During a visit to Trump Tower in New York during Trump’s transition to the presidency, Ivanka Trump greeted Abe at the elevator and escorted him to her father’s office, where she participated in the meeting with Kushner. Abe chatted with Ivanka Trump over Arabella’s fascination with Pikotaro. And again, after she and her children visited the embassy in April, Abe raised the event as an icebreaker in his phone conversation with President Trump a day later.

Ivanka Trump has returned the gesture with subtle signals to the Japanese of her attention to their culture. This month on Instagram, she posted a short video of a private moment of dancing with her two young sons in their kitchen, delighting Japanese Embassy officials by choosing Pikotaro’s latest tune, “I like O.J.”

Ivanka Trump’s emerging role as an official and unofficial emissary to her father’s government has sparked some controversy at home and abroad. But it is not entirely unusual.

Carl Anthony, a historian with the National First Ladies’ Library, said her role is similar to those of other first daughters who were deputized by their fathers to step into areas where, at times, the first lady could not or would not go.

“The first lady role, when you really break it down, consists of about seven or eight different kind of roles,” Anthony said. “What you’ve had on occasion, but not really in our lifetime, is more than one woman in the family assuming some of the roles, but not others.”

Theodore Roosevelt deputized his daughter Alice on a months-long diplomatic mission to three Asian countries, where she was dubbed a “princess.” Julie Nixon Eisenhower became a liaison on environmental issues for her father, Richard Nixon. And Franklin D. Roosevelt chose his daughter Anna to accompany him to the Yalta conference toward the end of World War II, where she met with foreign dignitaries but primarily served as a source of encouragement and support for her father.

“Ivanka’s role is ineffable,” Anthony said. “It’s knowing her father’s chemistry. It’s knowing how to approach him and when to approach him. It’s choosing her battles carefully and knowing how to frame her, perhaps, disagreement on something.”

Correction: An earlier version of this story incorrectly stated that Ivanka Trump’s mother is half Czech.