Republican senator sets conditions for backing START

* Modernizing U.S. nukes will cost billions more, Kyl says

* He's undecided on the new START treaty

By Susan Cornwell

WASHINGTON, Aug 4 (Reuters) - President Barack Obama must show greater commitment to modernizing the U.S. nuclear arsenal to gain Republican support for an arms control treaty with Russia, the Senate's No. 2 Republican said on Wednesday.

Senator Jon Kyl denied setting a price to support the strategic arms reduction pact known as the "new START." But he told reporters the commitment he was seeking could cost up to $10 billion more than the amount the administration has pledged to modernizing U.S. nuclear weapons.

Obama wants the treaty ratified this year but it needs 67 votes in the Senate, meaning it cannot pass without substantial Republican support.

Kyl's demands would be difficult to meet by the end of the year. He wants Congress to appropriate extra funds and he also wants to see administration budget plans.

Kyl said Republicans were seeking "a more precise and higher degree of commitment" to modernizing the U.S. nuclear arsenal, "so that we know that this program is not going to go for a while and peter out."

Obama signed the strategic arms agreement with Russian President Dmitry Medvedev in April and sent it to the Senate in May. It commits the former Cold War foes to reducing deployed nuclear warheads by about 30 percent; Obama cast it as a first step toward his goal of a world without nuclear weapons.