Barack Obama and leaders of the G7 group of nations have threatened Russia with more sanctions if it continues to undermine the sovereignty of Ukraine and fund separatists in the east of the country.

The US president issued the warning on Thursday and urged his Russian counterpart Vladimir Putin to hold direct talks with the Ukrainian president-elect Petro Poroshenko to end the crisis.

"The kinds of destabilising activities funded and encouraged by Russia are illegal and not constructive," Obama said in Brussels after a meeting of G7 leaders.

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"There is a path in which Russia has a capacity to engage directly with President Poroshenko now. He should take it."

Obama said Russia must help stop the flow of arms into Ukraine, and exert its influence to stop further separatist operations.

"If Mr Putin takes those steps, then it is possible for us to begin to rebuild trust between Russia and its neighbours and Europe," Obama said. "We will have a chance to see what Mr Putin does over the next two, three, four weeks, and if he remains on the current course, then we've already indicated that kinds of actions that we are prepared to take."

The British prime minister, David Cameron, said Putin must meet the conditions in the next month.

"If these things don't happen, then sectoral sanctions will follow," he said.

"The next month will be vital in judging if President Putin has taken these steps," said Cameron, who later met Putin in France.

Al Jazeera's James Bays, reporting from Brussels, said: "The G7 leader are talking here again about tougher sanctions on Russia. But they are talking about the same tougher sanctions they have been talking about for months now."

Border posts seized

Meanwhile, pro-Russian fighters are said to have taken control of all border posts in the eastern Ukrainian town of Luhansk.

Al Jazeera's David Chater, reporting from the town said that government forces had been "outgunned, outnumbered and overwhelmed" and had been cut off from their chain of command.

"This is humiliating for Ukraine," Chater said, adding that the eastern borders were now unguarded, allowing the flow of arms.

Ukrainian authorities have closed three checkpoints along the border with Russia after nightly assaults by separatists.

The authorities said three checkpoints - at Chervonopartyzansk, Dolzhansky and Chervona Mogyla - had been temporarily closed, and that the Russian side had been notified.

Source: Al Jazeera and agencies