ISLAMABAD (Reuters) - Pakistani called on the United States on Sunday to share information about new al Qaeda leader Ayman al-Zawahri after U.S. Defense Secretary Leon Panetta said he believed that Osama bin Laden's successor was in Pakistan.

During his first trip to Kabul on Saturday as Pentagon chief, Panetta said he believed that the new al Qaeda leader was living in Pakistan's lawless tribal belt on the Afghan border.

The Pakistani military said its troops were already carrying out "intense operations" against al Qaeda and its affiliates as well as "terrorists leadership" and high value targets (HVTs) who pose a threat to Pakistan's security.

"We expect U.S. intelligence establishment to share available information and actionable intelligence regarding Al Zawahri and other HVTs with us, enabling Pakistan Army to carry out targeted operations," a military spokesman said in a statement.

The former CIA chief said the strategic defeat of al Qaeda was within reach if the United States could kill or capture up to 20 remaining leaders of the core group and its affiliates.

He said these militant leaders were living in Pakistan, Yemen, Somalia and in North Africa.

Panetta said now was the time -- in the wake of bin Laden's killing in Pakistan in May -- to intensify efforts to target al Qaeda leadership, adding that the United States would like Pakistan to target Zawahri in the tribal areas.

Pakistan is an important U.S. ally, but relations have been seriously damaged after U.S. Navy SEALs killed bin Laden in a secret raid in the Pakistani military town of Abbottabad without informing Islamabad in advance.

The United States has also stepped up missile strikes by remotely-piloted drone aircraft in Pakistan's ethnic Pashtun tribal lands, long regarded as a global hub of militants.

Pakistan publicly criticizes drone strikes and often demands the United States provide intelligence on militant leaders hiding in its tribal regions so it can take action against them.

However, there have been persistent suspicions in Washington that Pakistani intelligence agencies maintain ties with these militants.

U.S. media last month reported that Panetta confronted Pakistan with evidence that militants had vacated bomb-making factories in Waziristan after the Unites States shared intelligence with Pakistan, suggesting that it had tipped off the insurgents.

The Pakistan army denied the reports.

(Reporting by Zeeshan Haider; Editing by Chris Allbritton and Sugita Katyal)