* Putin says U.S. sanctions harm ties, stability
* First telephone conversation since flight MH17 downed (Adds Obama comments from news conference)
By Roberta Rampton and Thomas Grove
WASHINGTON/MOSCOW, Aug 1 (Reuters) - U.S. President Barack Obama phoned Russia's Vladimir Putin to urge him to stop supporting separatists in Eastern Ukraine and seek a diplomatic solution to the crisis that has spurred tough new economic sanctions.
Obama told reporters on Friday he believes the United States has done "everything that we can do," short of going to war, to deter Russia from further threats to Ukraine with the sanctions on its energy, defense and financial sectors.
"President Putin should want to resolve this diplomatically. Get these sanctions lifted, get their economy growing again, and have good relations with Ukraine," Obama said during a news conference.
"But sometimes people don't always act rationally, and they don't always act based on their medium- or long-term interests," he said.
It was the first conversation between the two leaders since July 17, when a Malaysian passenger jet was shot down over eastern Ukraine by what U.S. officials believe was a missile launched by pro-Russian separatists.
During the call, Putin told Obama that the measures were "counterproductive," a statement from the Kremlin said.
"The Russian leader described Washington's course of ramping up sanctions pressure as counterproductive, causing serious damage to bilateral relations and international stability in general," the Kremlin said.
The Kremlin statement said "significant differences" remained between the two leaders but that both emphasised the importance of an "immediate and sustained ceasefire" in east Ukraine.
The two leaders agreed to keep open their channels of communication, the White House said.
Ties between the United States and Russia have plunged to their lowest level since the end of the Cold War over the Ukraine crisis, which Washington accuses Moscow of fanning with weapons and support.
During the call, Obama also raised his concerns about what Washington says was a violation by Russia of the 1988 Intermediate-Nuclear Treaty designed to eliminate ground-launched cruise missiles, the White House said.
The U.S. government pledged about $8 million in new aid on Friday to bolster Ukraine's border guard service, a promise made by Vice President Joe Biden in a phone call with Ukraine President Petro Poroshenko.
The aid includes engineering and surveillance equipment, transport and patrol vehicles, and small boats, the White House said in a statement. (Additional reporting by Steve Holland and Mark Felsenthal in Washington; Editing by Ruth Pitchford and Ken Wills)