"Most options ought to be on the table," short of invasion by US forces, the Democrat senator said.
The US and Britain have announced plans to fund Yemen's counterterrorism police force, but Barack Obama, the US president, has explicitly ruled out sending in troops.
Mohamed Vall, Al Jazeera's correspondent in Sanaa, Yemen's capital, said that the religious leaders' decision to oppose any military intervention would carry great weight in the country.
"In a highly conservative, highly religious society like Yemen, it is the word of the clerics and not that of the politicians that really resonates among the masses. And today the clerics of Yemen have announced their verdict," he said.
The clerics said that their opinion was in line with that of most Yemenis and the Sanaa government, while also criticising the killing of foreigners in an apparent allusion to suspected al-Qaeda attacks.
The Yemeni government, which is also fighting a rebel group in the north of the country, and a secessionist movement in the south, has said it is engaged in an "open war" to clear al-Qaeda fighters from its territory.
"The war security forces launched against al-Qaeda elements is open whenever or wherever we find these elements," a government news website reported on Thursday, quoting an unnamed security source.
It said the source had also warned Yemenis against "hiding any al-Qaeda elements".
Sanaa has repeatedly denied that it will require foreign intervention to help it defeat the movement, an amalgamation of groups from Yemen and Saudi Arabia.
"Yemen is not Afghanistan, nor Pakistan, where terrorists constantly launch attacks while the authorities try to respond," Ali Anisi, Yemen's head of national security, said on Wednesday.
"Here, we anticipate the threat. Yemen is not a hideout for the terrorists and will never be."
Robert Grenier, a former CIA station chief in Pakistan who also headed the Iraq Issues Group during the Bush administration, told Al Jazeera: "One of the difficulties that [the Americans] see in Yemen, as we see in many other places, is unrepresentative, corrupt and repressive government.
"At the end of the day, the only real solution to the problem of terrorism is to have responsible government, with the willingness and the ability to control its own territory.
"There are many who are inclined to view the Ali Abdullah Salehs [president of Yemen] of the world as American puppets. In fact, maybe unfortunately, it is far from that. ... He is serving his own interest. [However], there aren't really many good alternatives."
Yemen has insisted that it is making advances against al-Qaeda, citing air raids in December that killed more than 60 people and a string of reported arrests of suspected al-Qaeda figures.
However, Al-Qaeda in the Arabian Peninsula has used the air raids to encourage anti-American feeling, claiming that they were carried out by US warplanes.