Western leaders have announced that the Russian president, Vladimir Putin, had a matter of weeks to stop destabilising Ukraine and seek a settlement with his new counterpart in Kiev or face much more wide-ranging economic sanctions.

A G7 summit in Brussels – from which Russia was excluded for the first time in 16 years – ended with the leaders of Britain, France, Germany and the US preparing to confront Putin in person for the first time since the Ukraine crisis turned violent in February.

The British prime minister, David Cameron was to meet Putin in Paris on Thursday night as the leaders moved from Brussels to France to mark the 70th anniversary of the D-day landings. In separate meetings, Putin was due to talk to Cameron, Chancellor Angela Merkel of Germany, and President François Hollande of France.

Although no formal session was scheduled between Putin and Barack Obama, the US leader said: "I have no doubt that I'll see Mr Putin. And he and I have always had a businesslike relationship … Should we have the opportunity to talk, I will be repeating the same message that I've been delivering to him throughout the crisis."

Following the landslide election of Petro Poroshenko as Ukraine's new president, western leaders are tentatively hopeful of a diplomatic breakthrough that could produce direct talks between Moscow and Kiev. Putin has recognised the legitimacy of the election, but not the legitimacy of Poroshenko as Ukraine's president, who is to be sworn in on Saturday.

"His inauguration provides an opportunity," said Obama. "Russia needs to seize that opportunity. Russia needs to recognise that president-elect Poroshenko is the legitimately elected leader of Ukraine, and engage the government in Kiev. Given its influence over the militants in Ukraine, Russia continues to have a responsibility to convince them to end their violence, lay down their weapons and enter into a dialogue with the Ukrainian government. If Russia's provocations continue, it's clear from our discussions here that the G7 nations are ready to impose additional costs on Russia."

Obama spoke of weeks, not months, and highlighted sanctions hitting entire sectors of the Russian economy, although the issue is divisive between both sides of the Atlantic because the Europeans would suffer from Russian retaliation, while the US is relatively unexposed to Russian retribution.

Cameron declared that he would tell Putin there were certain things that had to happen. "The continuing destabilisation of eastern Ukraine must stop. President Putin must recognise the legitimate election of President Poroshenko. He must stop arms crossing the border into Ukraine. He must cease Russian support for separatist groups. If these things don't happen, then sectoral sanctions will follow. The next month will be vital in judging if President Putin has taken these steps."

The warnings were echoed by Merkel and Herman Van Rompuy, the president of the European council chairing the G7 summit. Despite the talk of sectoral sanctions against Russia, Hollande has refused to cancel or freeze billions in military contracts with Moscow for fear of being sued and of the impact on jobs at home. Obama was mildly critical.

"I recognise that the jobs in France are important. I think it would have been preferable to press the pause button," he said.

Senior European officials said the smooth election of Poroshenko may have changed the equation in Ukraine, supplying a chance for a diplomatic and political breakthrough with Russia.

Obama called on Putin to "seize this moment" and also held out the prospect of conditional rapprochement.

"We are at a point where Mr Putin has a chance to get back into a lane of international law," he said. "If Mr Putin takes those steps, then it is possible for us to begin to rebuild trust between Russia and its neighbours and Europe.

He added: "We can't simply allow drift. The mere fact that some of the Russian soldiers have moved back off the border and that Russia is now destabilising Ukraine through surrogates rather than overtly and explicitly does not mean that we can afford three months or four months or six months continued violence and conflict in eastern Ukraine. We will have a chance to see what Mr Putin does over the next two, three, four weeks."