President Obama waves as he boards a plane to leave Belgium at the military airport in Melsbroek on June 5. (Eric Lalmand/AFP/Getty Images) (Eric Lalmand/AFP/Getty Images)

President Obama on Thursday said Russia now has a chance to resolve the Ukrainian crisis and rebuild trust with the West but warned Russian President Vladimir Putin that his country would face harsher sanctions if he fails to take steps to support stability in Ukraine.

“If he continues a strategy of undermining the sovereignty of Ukraine, then we have no choice but to respond,” Obama said at a news conference with British Prime Minister David Cameron following a meeting of the Group of Seven major developed nations here. Cameron expressed the same view.

Obama said Putin has an opportunity “to seize this moment” and turn the page. He said he was pleased to see Putin not denounce the May 25 election of Petro Poroshenko as Ukraine’s new president, saying it “offers the prospect that he’s moving in a new direction.”

But if Putin “remains on the current course, we’ve already indicated the kinds of actions we could take,” Obama warned, suggesting a wider deployment of sanctions targeting broad sectors of the Russian economy — beyond the existing sanctions that target only individuals or specific companies.

Obama and Cameron suggested that Putin has about until the end of the month to make a choice about whether he will change course in Ukraine.

In his remarks, Cameron said Russia had lost its seat in the Group of Eight — which has now effectively reverted to its former status as the G-7 — because of actions that are “totally at odds with the values of this group of democracies.” The British prime minister seemed to offer specific criteria for applying stricter sanctions: the end of Russian support for separatists operating in eastern Ukraine and the recognition of the Poroshenko government.

“If these things don’t happen, then sectoral sanctions will follow,” Cameron said.

Speaking later aboard Air Force One, U.S. officials made clear that certain escalatory actions — such as Russian troops crossing the border into Ukraine — would trigger more punitive measures. But they would not define exactly what Putin would have to do to avoid further sanctions. Nor would they set an exact deadline.

“Clearly sectoral sanctions are on the table,” said Ben Rhodes, deputy national security adviser for strategic communications. “If we see the status quo continuing, we are going to move to additional sanctions. . . . We’ll be calibrating those based on what the situation is.”

Many in Eastern Europe have worried that the West would not impose additional punishments if the crisis continues.

Obama was speaking after wrapping up two days of meetings with leaders from six other world powers. The G-7 summit that began Wednesday night focused on the crisis in Ukraine and policy toward Russia, which was pointedly excluded from the gathering after its annexation of Ukraine’s autonomous Crimea region in March.

Obama credited existing sanctions with harming Russia’s economy, though he acknowledged that it would be a challenge to figure out how to devise harsher sanctions without also harming Europe’s economies.

Obama and Cameron both acknowledged there would be challenges in rallying all the European nations to favor stricter sanctions.

“Do I expect unanimity among the 28 E.U. members?” he asked. “I’ve now been president five and a half years, and I’ve learned a thing or two about the European Union.”

Cameron and French President Francois Hollande were set to meet with Putin in Paris on Thursday — meetings that the British prime minister described as a reasonable way to keep the lines of other communications open.

Obama has made clear he has no plans to meet with Putin and expressed a desire for the Western allies to speak with a unified voice, although the two leaders are expected to cross paths while attending D-Day commemorations in Normandy on Friday.

“I have no doubt that I’ll see Mr. Putin, and he and I have always had a businesslike relationship,” Obama said. “I will be repeating to him the same message I’ve been delivering to him throughout this crisis.”

In any case, Secretary of State John F. Kerry met with Russian Foreign Minister Sergei Lavrov in Paris on Thursday and reiterated U.S. hopes that Moscow would recognize the new Ukrainian government and hold talks with it. The goal, he said, is for Ukraine not to be “the pawn in a tug-of-war between other nations, but rather an independent, sovereign country with the integrity of its borders and people.”

Lavrov replied that he would also like to see Ukraine as peaceful and stable. He added: “The Russian-American agenda is much broader than just Ukraine. We would like to see other countries like Iraq, Libya, Syria, many others, also to be in peace, not to be used as a pawn, and I hope that we can discuss all these things.”

On Thursday evening, Cameron and Putin were scheduled to meet at Charles de Gaulle Airport. Obama was set to have dinner with Hollande later Thursday. After that, Hollande was scheduled to have another dinner with Putin.

Earlier on his European tour, Obama visited Poland and met with Poroshenko in Warsaw. Obama announced he would be sending $5 million in night-vision equipment and other nonlethal aid to assist Poroshenko in building up his country’s defense capabilities. Obama signaled he was open to providing more assistance, aides said.

Also while in Warsaw, Obama met with top Polish leaders and repeatedly pledged the United States’ unwavering commitment to the security of Eastern Europe, culminating in a high-profile speech at the celebration of Poland’s first 25 years of democracy.

Poland and its neighbors have been deeply unsettled by Russia’s annexation of Crimea and its support for pro-Russian separatists in eastern Ukraine.

“Russia needs to recognize that President-elect Poroshenko is the legitimately elected leader of Ukraine,” Obama said Wednesday. “Given its influence over the militaries in Ukraine, Russia continues to have a responsibility” to work to bring stability to the country.

In recent days, tensions have cooled somewhat because the May 25 elections in Ukraine went relatively smoothly and Russia has moved troops away from its border with Ukraine. Still, following the G-7 meeting Wednesday night, world powers issued a stern warning to Putin.

“We are united in condemning the Russian Federation’s continuing violation of the sovereignty and territorial integrity of Ukraine. Russia’s illegal annexation of Crimea, and actions to de-stabilize eastern Ukraine are unacceptable and must stop,” read a G-7 communique released late Wednesday. “We stand ready to intensify targeted sanctions and to implement significant additional restrictive measures to impose further costs on Russia should events so require.”