US President Donald Trump stressed the importance of the Seoul-Washington alliance and held in-depth talks over North Korea's nuclear problems during his summit with Chinese counterpart Xi Jinping, the office of South Korea's acting leader said Saturday.

Trump made the remarks during his 20-minute phone conversation with Acting President and Prime Minister Hwang Kyo-ahn which started at around 7:20 a.m. after his first summit with Xi.

"(Trump told Hwang) that there were in-depth discussions about North Korea's serious nuke problems and how to respond to them (during the summit)," according to Hwang's office.

"(The US president said that) he delivered Washington's stance to China over the deployment of an advanced US missile defense system in South Korea," it said.

The phone talks came after Trump and Xi agreed Friday to work together closely to convince North Korea to curb its nuclear program in their summit talks.

There is speculation that North Korea may carry out another nuclear test or launch a long-range rocket around its key anniversaries in April including the birthday of late founder Kim Il-sung on April 15.

Trump said he sufficiently emphasized to Xi the importance of South Korea and the Seoul-Washington alliance, the office said.

"(The US President said that) during the summit, considerable time was spent in discussing issues of the Korean Peninsula," it said.

In response, Hwang stressed that South Korea and the US should further strengthen close coordination against North Korea's possible provocations.

"I believe (the latest summit) seemed to be an occasion to reaffirm the strong alliance between Seoul and Washington," the acting president said.

Trump showed support for South Korea's policy toward North Korea, vowing close cooperation to resolve North Korea's nuclear standoff.

The summit also came amid China's strong opposition to Seoul and Washington's ongoing deployment of the Terminal High Altitude Area Defense on South Korean soil.

China showed an explicit objection to the THAAD installation, saying that the move undermines China's security interests.

The Seoul government viewed the latest phone talks as evidence supporting that high-level communication channels between the allies are smoothly working even in the midst of a leadership vacuum left by the ouster of former President Park Geun-hye.

Trump discussed North Korea's launch of a ballistic missile with Japanese Prime Minister Shinzo Abe over phone on Wednesday.

But there were no phone talks with Hwang, sparking concerns that Seoul may be left out of discussions in response to Pyongyang's nuke and missile issues.

Hwang and Trump also agreed to have more follow-up discussions and maintain strong coordination by using US Vice President Mike Pence's planned trip to Seoul later this month and other talks of high-level officials between the two countries, according to the office.

Meanwhile, the US and China agreed on efforts to resolve North Korea's nuclear issue, but they did not go so far as to issue a joint statement in an indication that there was no major breakthrough over the matter.

"China has a red line which means that its employment of sanctions against North Korea should not be stringent enough to lead to North Korea's collapse," said Kim Hyun-wook, a professor at the Korea National Diplomatic Academy. "Washington seems to have failed to break China's threshold this time."

Major political parties in Seoul welcomed that the two leaders met and affirmed their shared concern over the North's nuclear threat but still expressed disappointment with their apparent failure in making marked progress in coming up with a solution.

"The Trump administration's first summit with China held for two days in the US ended with little progress on how to resolve the North's nuclear problem," Park Kwang-on, a spokesman for the Democratic Party's leading presidential contender Moon Jae-in, said in a comment.

"It is still noteworthy in that the leaders of the two countries shared the understanding of the seriousness of the North's nuclear issue," he added. "We expect the two will make serious efforts going forward in finding a solution to the problem."

Kim Kyung-jin, a spokesman for the centrist People's Party, also echoed the opinion, saying that it is "disappointing" in that they failed to produce any solution other than to share the concern that the North's nuclear issue is a "serious" matter. (Yonhap)