(Adds McCain statement, background)
WASHINGTON, March 1 (Reuters) - U.S. Defense Secretary Chuck Hagel spoke on Saturday with his Russian counterpart, a U.S. official told Reuters, as Russian President Vladimir Putin secured his parliament's authority to invade Ukraine.
Asked whether some U.S. military units had been on alert over turmoil in the Crimean peninsula, the official said there was no change in the U.S. military's stance. The U.S. focus was on diplomatic options, said the official, who spoke on condition of anonymity.
The official gave no details of Hagel's conversation with Russian Defense Minister Sergei Shoigu.
Putin was given quick authority on Saturday by Russia's parliament to invade Ukraine after troops seized control of the Crimea peninsula.
The developments came a day after Obama had warned that there would be "costs" if there was military intervention by Russia in Ukraine, where Moscow ally President Viktor Yanukovich was ousted last week.
U.S. Senator John McCain, a leading Republican voice on foreign affairs who often advocates a more forceful approach by Washington, called on Obama on Saturday to "articulate exactly what those costs will be and to take steps urgently to impose them."
"Every moment that the United States and our allies fail to respond sends the signal to President Putin that he can be even more ambitious and aggressive in his military intervention in Ukraine," McCain said in a statement.
"There is a range of serious options at our disposal at this time without the use of military force."
Another leading Senate Republican, Bob Corker, called on Obama to lead an international response that could include sanctions. (Reporting by Phil Stewart; Editing by Bill Trott and Frances Kerry)