(Reuters) - India's navy withdrew two warships from the eastern port of Kolkata on Tuesday after intelligence agencies warned of an attack on the port and the city, police and navy officers said.

The rare move came two days after a suicide bomber killed 60 people on the Pakistani side of the main border crossing with India hundreds of miles to the west, deepening fears that Pakistan's internal strife was spreading into India.

Two naval warships, INS Khukri and INS Sumitra, that had docked in Kolkata on Monday were ordered back into sea for "operational reasons", navy spokesman Captain D.K. Sharma said.

The ships were meant to be in port until Friday for public viewing as part of ceremonies in the run-up to Navy Day next month, he said.

Two officers in the control room at the police headquarters in West Bengal where Kolkata is located said they had received a message from federal intelligence agencies on Tuesday warning of the possibility of an attack on the port.

"The alert is for the port area. We have taken security measures following the alert," the inspector in charge of the state control room said, asking that he not be named in line with state police policy.

On Sunday, a bomber detonated his suicide vest near the Wagah checkpoint between Indiaand Pakistan just as people on the Pakistani side were leaving after a daily flag-lowering ceremony by border guards.

Three Pakistan-based groups including a splinter faction of the Pakistan Taliban with ties to al Qaeda claimed responsibility for that attack, the deadliest in months in Pakistan's heartland Punjab province.

While the attack was seen immediately as a reprisal for Pakistani army operations against militants sheltered in North Waziristan, intelligence experts in India said the location of the attack near the border had touched off alarm bells.

"The Pakistanis have been hit, but there is a message for us. It is near to the Indian border, we cannot but take cognizance," said Rana Banerji, a former top official at the Research and Analysis Wing, India's external intelligence arm and a long-time specialist on Pakistan and militant groups.

Both Pakistan and India have been on higher alert since al Qaeda announced the formation of a local branch to raise the flag of jihad in a region home to more than 400 million Muslims.

Days after the announcement by its chief Ayman al-Zawahri last month, al Qaeda's South Asia wing claimed responsibility for hijacking a Pakistani naval ship and trying to use it to fire rockets at U.S. vessels in the Arabian Sea, in the first major assault by the newly created group.

The attack in the southern port of Karachi was repelled after a six-hour exchange of fire.