Tillerson's potential no-show had increased unease caused by U.S. President Donald Trump's description of NATO as "obsolete" during his election campaign.
Although it was unclear how the zones would work, safe havens could ratchet up U.S. military involvement in Syria and mark a departure from President Obama's more cautious approach.
Tillerson argued that Montenegro's membership in the alliance would support greater integration, democratic reform, trade, security and stability among its neighbors.
A North Korean spokesperson said the North would push forward with its nuclear plans.
The decisions to skip the NATO meeting and to visit Moscow risked feeding a perception that Trump may be putting U.S. dealings with big powers before those of smaller nations.
The secretary of state and President Trump have been critical of China in recent weeks.
"It will happen," Republican Senator Richard Burr told reporters after a closed committee meeting.
Chances of Tillerson persuading China to do more to curb North Korea's weapons programs appear scant, given China's anger at the deployment of a U.S. anti-missile system in South Korea.
New York's attorney general said it found Tillerson had used an email address under the pseudonym "Wayne Tracker" for at least six years.
Greenpeace argued in its letter that Exxon Mobil would "directly and predictably" benefit from the approval of Keystone XL because the firm has investments in Canadian oil sands.
The experienced diplomat takes the role amid investigations into Trump's ties with Russia.
Tillerson declined to unveil the report in person, breaking with precedent established during both Democratic and Republican administrations.
China's state news agency, Xinhua, quoted Yang as saying China was willing to work with Washington "to enhance exchanges on all levels from top down" and to broaden communication and coordination on regional and global issues, while respecting "each other's core interests and major concerns."
The U.S. government this week angered Mexico by saying it was seeking to deport many illegal immigrants to Mexico if they entered the United States from there, regardless of their nationality.
The U.S. Department of Homeland Security unveiled plans on Tuesday to consider almost all illegal immigrants subject to deportation.
The call appeared to be the latest effort by the world's two largest economies to put relations back on an even keel after a rocky start following U.S. President Donald Trump's November election victory.
The successful intervention by Tillerson, suggests that in a White House-dominated administration, the new secretary of state could help drive decisions on some geopolitical issues.
Within hours of starting the job, Tillerson reached out by phone to counterparts from Mexico and Canada, and met with German Foreign Minister Sigmar Gabriel, department officials said.
As former Exxon Mobil CEO Rex Tillerson takes over the State Department, anti-corruption rules may be overturned before they go into effect.
Despite concerns about the former Exxon Mobil CEO's ties to Russia, he won a 53-42 vote.
Under Secretary for Management Patrick Kennedy and acting Under Secretary of State for Arms Control and International Security Thomas Countryman both plan to leave their posts by Friday, the officials said.
The U.S. Senate Foreign Relations Committee voted 11-10 to approve Tillerson, with every committee Republican backing Tillerson and every Democrat opposing his nomination.