Russia said it has invited monitors from the OSCE European security and rights body to two of its borders crossings with Ukraine, as a "sign of good will", the foreign ministry said.
Russia has been building up its forces on the Ukrainian border steadily over the past few weeks and now has an estimated 10-12,000 troops in the area, a Nato military officer said.
Russia had withdrawn the majority of the 40,000 troops it had on the border earlier this year, and there were fewer than 1,000 by the middle of June. Speaking on the condition of anonymity, the officer told Reuters:
"Our current assessment is that between 10,000 and 12,000 troops are now in the area ... In the last week alone, we have seen several units moving into the border region."
German Chancellor Angela Merkel and Russian President Vladimir Putin agreed that the Ukraine situation "has a tendency towards degradation" and have urged greater peace efforts, Putin's spokesman Dmitry Peskov has said.
He said: "Both Putin and Merkel stressed the necessity to urgently resume the work of a contact group on Ukraine.
"It is their common opinion that, in order for the contact group to resume its work, a ceasefire needs to be declared as soon as possible," Peskov said.
The two leaders met briefly before the World Cup final in Brazil.
Ukraine has called an accusation its forces fired across the border "total nonsense".
Kiev suggested the attack, which is said to have killed one person, could have been the work of rebels trying to provoke Moscow to intervene on their behalf. The rebels denied they were responsible.
Inside Ukraine, combat has intensified dramatically since a rebel missile attack that killed dozens of government troops on Friday.
Local officials said on Sunday 18 people were killed in shooting incidents in the two main rebel-held cities.
Ukrainian President Petro Poroshenko will not be appearing at the World Cup in Brazil following reports he may be due to meet Russian leader Vladimir Putin at the final.
A statement said Mr Poroshenko had received an invite from Brazil's President Dilma Rousseff, but felt it was "impossible" to justify the visit "given the situation that is happening in Ukraine".
Russian President Vladimir Putin could meet his Ukrainian counterpart Petro Poroshenko on the sidelines of the World Cup final in Brazil, although no talks were being planned at this point, a spokesman for the Kremlin has said.
"We are not preparing any separate meetings. As far as we know, he is going there too," said Kremlin spokesman Dmitry Peskov in the Argentine capital Buenos Aires.
"There will be some separate room for leaders at the stadium, and therefore one of course cannot rule it (meeting) out," he said on the sidelines of a meeting between Putin and Argentina's president, Cristina Fernandez.
A Ukrainian shell that reportedly hit the border town of Donetsk could have "irreversible consequences", Russia's foreign ministry has warned.
According to Russian news agencies, the shell hit a residential building, killing one person and injuring one other.
Russia said the fatality was the result of an "aggressive act" against sovereign Russian territory and against Russian citizens.
The foreign ministers of Ukraine, Russia, Germany and France will meet in Berlin today to try to make progress on resolving the crisis in eastern Ukraine, according to a French diplomatic source quoted by Reuters.
"There is not a precise objective. It's an opportunity to work on peace efforts, but we don't want to raise expectations," the source said.
Ukraine's President says he has decided to lift a ceasefire because "terrorist" pro-Russian separatists had violated the agreement.
"We will attack and free our lands. The decision not to continue the ceasefire is our answer to terrorists, militants and marauders," Petro Poroshenko said.
The Ukrainian authorities said 27 of their military personnel had been killed since the beginning of the ceasefire on June 20th.
Ukrainian president Petro Poroshenko says the country's forces will "attack and free our lands", as he ended a ceasefire with pro-Russian separatists.