They both have advanced degrees, but they come from different worlds. Ashraf Ghani, who earned a doctorate from Columbia University, is a former academic and World Bank official. Abdullah Abdullah, who earned a medical degree from Kabul University, is a former resistance figure who fought against the Soviet occupation and the Taliban.

On Monday, after months of political tensions, the unlikely pair took their oaths of office to lead a U.S.-brokered coalition government in Afghanistan’s first democratic transfer of power. Ghani became the country’s new president. He then swore in Abdullah as his chief executive.

Only a few weeks ago, Ghani and Abdullah were at odds over an election that threatened to split Afghanistan’s ethnic groups and trigger violence. Both claimed victory in the vote held to succeed President Hamid Karzai, who came to power after U.S.-backed Afghan forces toppled the Taliban in 2001. The two rivals relented only after the United States stepped in to carve out a compromise deal.

Now, many Afghans and Western diplomats hope that the two can set aside their differences and address their nation’s numerous challenges, including rampant corruption, high unemployment and growing security threats.

Ghani and Abdullah are taking charge as most foreign troops are scheduled to withdraw by year’s end and the Taliban is resurging in many areas of the country. Afghanistan’s central government is also nearly broke and can barely pay the salaries of its federal and provincial employees.

Afghanistan's new President Ashraf Ghani Ahmadzai, right, and Afghanistan's Chief Executive Abdullah Abdullah take the oath during their inauguration in Kabul on Sept. 29. (Omar Sobhani/Reuters)

“These two guys with different philosophies and ideas, and coming from different regions, ethnic and educational backgrounds, do not seem like they will merge easily,” said Farouq Bashar, a political analyst and lawyer. “These two may not easily accept candidates for government positions from each side. Everyone has their own commitment to their followers.”

At Monday’s inauguration ceremony at the presidential palace in central Kabul, Ghani and Abdullah promised to work together for Afghanistan’s progress. In the audience were hundreds of dignitaries from 34 countries, as well as the United Nations and the European Union. John Podesta, a senior adviser to President Obama, led the U.S. delegation, which included Ambassador James B. Cunningham and other senior officials.

“I am your leader, but I am not better than you. If I make mistakes, hold me accountable,” Ghani said in his address.

“Our commitment will be fulfilled together as a unified team to create national unity,” Abdullah said in his address.

Just as the ceremony began, a suicide bomber struck near a checkpoint close to the Kabul airport, underscoring Afghanistan’s security woes. Four security personnel and three civilians were killed, said Seddiq Seddiqi, an Interior Ministry spokesman.

In his address, Ghani called upon the Taliban and another armed faction, Hezb-i-Islami, to enter “a political negotiation” with the new government, saying that “we are tired of fighting and our message is peace, but this does not mean we are weak.”

A Taliban spokesman rejected the overture, saying the group does not recognize Ghani as the new president.

“The presidential inauguration has no meaning to the Islamic Emirate of Afghanistan,” Zabiullah Mujahid, the spokesman, said in a phone interview, using the Taliban’s name for the country. “It is the project of the United States.”

Monday’s inauguration also marked the end of Karzai’s long presidency. In his final speech as president, Karzai told the audience that he would support Ghani and Abdullah and that he would be “at their service.”

Despite their promises of working together, lingering tensions between the two leaders were apparent. Abdullah nearly boycotted the inauguration over a dispute about office space and whether he would be allowed to address the dignitaries, an aide said. Cunningham helped end the squabble.

At a news conference after the ceremony, Podesta called the inauguration “a momentous day for the Afghan people” and said Ghani and Abdullah are “seasoned leaders” with the “will and capacity to work together.” He played down the disputes that unfolded the night before the inauguration.

“The most important thing is that President Ghani and Dr. Abdullah resolved their problems,” Podesta said. “Are there remaining tensions? Are there going to be remaining issues? One would be surprised if there weren’t. But I think they both have the commitment to work those things out, to build a structure where they could collaborate.”

On one front at least, Ghani and Abdullah appear unified: the relationship with the United States. A representative of the new unity government, Cunningham said, is expected to sign a bilateral security agreement on Tuesday that would allow about 10,000 U.S. troops to remain in the country after 2014 to train and advise Afghan security forces. Karzai had refused to sign the pact, further souring ties with Washington. But Ghani and Abdullah have said publicly that they would endorse the agreement swiftly.

“The U.S. government has a solid relationship with both President Ghani and Dr. Abdullah, forged over a long period of time,” Podesta said. “Both recognize the commitments, both financially [and] particularly the sacrifices that U.S. personnel have paid here in Afghanistan.”

“We’ve turned a page,” he added, referring to the U.S. relationship with Afghanistan.

On the streets of Kabul, residents in cafes and restaurants watched the inauguration, which was televised nationally. Many expressed optimism that the new government could solve the challenges facing the country.

“Dr. Ghani has a clean past, and he is well educated,” said Ahmad Mubashir, 33, a shopkeeper. “The root of all problems that Afghans face is economic hardship, and I think he is the guy who has the ability to solve this problem. Once he solves the economic problems, definitely security will improve.”

Sharif Hassan contributed to this report.