By Lesley Wroughton and Margarita Antidze

TBILISI (Reuters) - Secretary of State John Kerry told ex-Soviet Georgia that the United States would help it bolster its army as he reassured a close U.S. ally days before a NATO summit expected to focus on the threat a resurgent Russia poses.

Kerry, on his first visit to Georgia as Secretary of State, made the commitment ahead of a NATO summit in Warsaw on Friday at which members of the Western military alliance plan to announce action to deter possible Russian military aggression.

Georgia and former Soviet states such as Moldova and Ukraine have become increasingly concerned by Russia's intentions after the Kremlin annexed Ukraine's Crimea in 2014 and launched air strikes in Syria last year.

Moscow says such fears are unfounded and based on what it calls anti-Russian hysteria.

In a memorandum of understanding signed on Wednesday by Kerry and Georgian Prime Minister Georgy Kvirikashvili, the United States promised to bolster Georgia's ability to defend itself against potential threats.

That meant greater military and security cooperation, enhanced information sharing, and help building up defense capacity, such as improving combat readiness and supporting defense procurement, the document said.

Until now, U.S. security support has focused on training Georgian troops for operations in Afghanistan and Iraq.

"The United States stands firm in its commitment to Georgia’s sovereignty, independence, and territorial integrity within its internationally recognized borders," Kerry told reporters.

Georgia, which is crisscrossed by strategically important oil and gas pipelines, fought and lost a short war with Russia in 2008. Moscow then recognized two breakaway pro-Kremlin Georgian regions - South Ossetia and Abkhazia - as independent countries, though most other countries have not.

"Russia's occupation and militarization of parts of Georgia's territory are unacceptable," said Kerry. "We continue to call on Russia to fulfill its obligations under the 2008 ceasefire agreement, including a withdrawal of its forces to pre-conflict positions."

Moscow for its part has accused the West, notably Washington, of stirring anti-Russian feelings in former Soviet states it deems part of its own sphere of influence.

Kerry visits Ukraine next, on Thursday, before heading to Warsaw to join U.S. President Barack Obama for the NATO summit.

In Ukraine, Kerry's third visit there since Russia annexed Crimea, he will focus on the implementation of the Minsk peace accords and the country's reform agenda. It will be Kerry's first chance to meet new Prime Minister Volodymyr Groysman.

(Writing by Lesley Wroughton and Andrew Osborn; Editing by Larry King)