Story highlights State Department says 18 diplomatic posts will reopen on Sunday

Facilities in Yemen and Lahore, Pakistan, will stay closed for now

No link seen between the Pakistan threat and another one by al Qaeda that forced the wider closures

Obama says "we are not going to completely eliminate terrorism"

All but one of the U.S. diplomatic posts closed this week in a sweeping response to fears of a possible al Qaeda attack will reopen on Sunday, the State Department said.

The Obama administration closed 19 embassies and consulates throughout the Middle East and North Africa, and issued a worldwide travel alert due to the threat apparently linked to communications between leaders of the terror group.

The closures took effect on Sunday.

The embassy in Sanaa Yemen, where al Qaeda in the Arabian Peninsula in based, will remain closed due to continued concerns about a possible attack.

Separately, the State Department withdrew most of its diplomatic personnel from its consulate in Lahore, Pakistan, on Thursday, citing a "separate credible threat" and warned U.S. citizens against travel to Pakistan.

Diplomatic personnel were moved to the capital, Islamabad. The Lahore facility also will remain closed.

"We will continue to evaluate the threats to Sanaa and Lahore and make subsequent decisions about the reopening of those facilities based on that information," State Department spokeswoman Jen Psaki said in a statement.

"We will also continue to evaluate information about these and all of our posts and to take appropriate steps to best protect the safety of our personnel, American citizens traveling overseas, and visitors to our facilities," she added.

One U.S. official said there was no link between the broader terror threat and the reason for the action taken in Lahore. However, the official said it doesn't rule out a possible link to al Qaeda.

Most of al Qaeda's core leadership is believed to reside in Pakistan and Lahore known to be home to other extremists sympathetic to the group.

No U.S. diplomatic posts in Pakistan were closed as a result of the wider warning inked to al Qaeda.

In that case, CNN previously reported U.S. officials intercepted a message between al Qaeda leader Ayman al-Zawahiri and a top ally in Yemen, Nasir al-Wuhayshi, telling him to "do something" -- an inference to a terror plot.

Now, two U.S. officials tell CNN that in his communication with Zawahiri, Wuhayshi, who is the leader of Al Qaeda in the Arabian Peninsula, laid out a plan for a plot and then Zawahiri acknowledged the communication.

Wuhayshi, the officials said, was not asking for permission from Zawahiri -- but rather informing him of his plans.

This scenario -- that Wuhayshi presented Zawahiri with a plan -- was first reported Friday in the Wall Street Journal.

CNN has also learned that the al Qaeda leaders communicated via some kind of encrypted messaging system, with multiple points of entry to allow for various parties to join in.

Asked about his assessment of the terror group in light of the latest threat, President Barack Obama reiterated his conclusion that its core blamed for 9/11 is "on its heels."

But he restated that al Qaeda and other extremist groups "have metastasized" into regional organizations that can still threaten U.S. interests, including embassies.

"And that's exactly what we are seeing right now," Obama said, noting that anti-terror efforts are an ongoing process.

"We are not going to completely eliminate terrorism. What we can do is to weaken it and to strengthen our partnerships in such a way that it does not pose the kind of horrible threat that we saw on 9/11," he said.

The origin of the Pakistan threat was not clear but a separate official said it was "conceivable" Lashkar-e-Tayyiba was involved. Lahore is well-known as a base for that group, which is considered a terrorist organization by the United States.