New Delhi (CNN) Taking militants out with drones isn't simple, but it's the best strategy available to eliminate the threat of terrorists in Yemen , U.S. President Barack Obama said Sunday.

The administration's policy in the increasingly unstable country has come under scrutiny in recent days as the U.S.-backed government crumbled under pressure from Shiite Houthi rebels.

"Yemen has never been a perfect democracy or a island of stability," Obama said in New Delhi, where he's on a three-day state visit. He described the U.S. policy there -- "partnering and intelligence-sharing with that local government" -- as the best approach in a bad situation.

"The alternative would be for us to play whack-a-mole every time there is a terrorist actor inside of any given country," Obama said.

The unraveling security situation in Yemen -- the same country Obama cited as a model for his fight against ISIS terrorists -- has thrown the President's counterterror message into question.

In the capital, Sanaa, last week, the presidential palace was overrun by Houthi rebels and President Abdu Rabu Mansour Hadi announced he was resigning.

That's a problem for the United States, which has relied on the government in Yemen as an ally in battling the al Qaeda affiliate that's based there. A power vacuum could benefit al Qaeda in the Arabian Peninsula, the terrorist offshoot that U.S. officials consider the most dangerous branch of the global jihadi network.

Amid the uncertainty in Yemen last week, it was reported the U.S. had suspended its counterterror efforts there. Obama said definitively on Sunday those reports were wrong.

"We continue to go after high-value targets inside Yemen," he said.

Obama himself cited the U.S.-Yemen partnership when he announced in September he was going after ISIS terrorists in Iraq and Syria.

Explaining why he was ruling out sending American troops to fight ISIS, Obama said he was modeling his strategy after what he said were successful efforts in Yemen and Somalia to partner with governments to go after terrorists.

"This strategy of taking out terrorists who threaten us, while supporting partners on the front lines, is one that we have successfully pursued in Yemen and Somalia for years," Obama said on September 10. "It is consistent with the approach I outlined earlier this year: to use force against anyone who threatens America's core interests, but to mobilize partners wherever possible to address broader challenges to international order."

What that strategy relied on, however, was a strong partnership between the United States and the existing government in Yemen, led by Hadi. Hadi reorganized Yemen's military to better go after AQAP, a strategy that worked for a time. But the plan was waylaid when resources were diverted to battle the militant Houthis, a group of Shiites who say they feel marginalized in the majority Sunni country.

Obama was confident on Sunday that U.S. anti-terror efforts would continue in Yemen.

"What we have shown is that we can maintain the kind of pressure on these terrorist networks even in these kind of difficult environments," he said.