WASHINGTON — Russia has roughly doubled the number of its battalions near the Ukrainian border, Western officials said Monday, and could respond to the Kiev government’s gains there by launching a cross-border incursion with little or no warning.

Over the past several weeks, Russia has built up 17 battalions — totaling 19,000 to 21,000 troops, according to one Western estimate — into a battle-ready force of infantry, armor, artillery and air defense within a few miles of the border. In addition, it has vastly expanded its firepower, increasing the number of advanced surface-to-air missile units to 14 from eight, and deploying more than 30 artillery batteries, according to the officials.

The Kremlin’s intentions in increasing its military abilities remain unclear. President Vladimir V. Putin of Russia could be seeking to pressure Ukraine and the United States to agree to a political settlement that would grant the eastern provinces of Ukraine maximum autonomy. But Mr. Putin, Western officials fear, may also be developing the option to intervene more directly if it appears that the pro-Russian separatists in Ukraine are on the verge of defeat.

American intelligence experts say that the advance by Ukrainian government forces on Donetsk and other steps that the Ukrainian government is taking to regain territory in the east from the separatists might prompt Mr. Putin to send his forces across the border under the guise of a “peacekeeping operation.”