* Washington says monitor presence essential in Georgia
* June 30 deadline for pullout looms
* United States stresses strategic agenda with Russia
WASHINGTON, May 15 (Reuters) - Signaling U.S. frustration as Washington seeks better relations with Russia, the United States criticized Moscow on Friday for blocking a deployment plan for peace monitors in Georgia.
State Department spokesman Ian Kelly urged Moscow to change its stance on keeping monitors from Europe's top security and human rights watchdog in Georgia, which is a major conduit for the transit of Caspian gas and oil to Western Europe.
Russia briefly invaded Georgia last year.
"It is disappointing and we hope that Russia will reverse its stance," Kelly told reporters.
The Greek chair of the Organization for Security and Cooperation in Europe (OSCE) failed this week to get consensus over extending its mission in Georgia due to Russian opposition about language in the proposal.
Russia insisted that the language reflected its view of South Ossetia as an "independent" state -- a position that has been rejected by Georgia and not endorsed by any other country in the 56-nation group.
"We believe a monitoring presence in Georgia remains essential and hope Russia, which has acknowledged a need for monitors, will eventually accept Greece's reasonable and balanced proposal," Kelly said.
Russia sent in troops last summer to crush Georgia's move to retake the separatist South Ossetia region and then rejected an extension of the OSCE's 16-year-old monitoring mission in the former Soviet republic past Dec. 31, when it expired.
The monitors now face a June 30 deadline to pull out.
Kelly said Greece had worked hard to devise a compromise solution that avoided reference to South Ossetia's legal or political status.
"We ... are disappointed that Russia could not accept the Greek chairmanship's constructive status-neutral solution," he said.
Russian Foreign Minister Sergei Lavrov discussed the issue with U.S. Secretary of State Hillary Clinton last week on a visit to Washington. They downplayed tensions over Georgia and said the issue would not cloud cooperation in other areas, such as arms control.
Asked if the latest Russian moves on Georgia were bad news for U.S.-Russia relations, Kelly pointed to the broad bilateral agenda between the two countries.
"We are very disappointed by this failure to reach consensus, but we have an important strategic agenda with Russia that includes nonproliferation issues, counterterrorism issues, a growing trade relationship," he said.
"I don't see this as a bad omen necessarily," he added.
U.S. President Barack Obama and Russian President Dmitry Medvedev are set to meet in July, and officials on both sides are glossing over differences ahead of the summit. (Editing by Paul Simao)
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