SEOUL (Reuters) - North Korea has been condemned internationally for conducting its most powerful nuclear test yet, but, across the border, South Korean President Moon Jae-in is also attracting flak for his policy of pursuing engagement with Pyongyang.

FILE PHOTO: South Korean President Moon Jae-In speaks during a press conference marking his first 100 days in office at the presidential house in Seoul, South Korea August 17, 2017. REUTERS/JUNG Yeon-Je/Pool/File photo

Rebuked by U.S. President Donald Trump, Moon is facing growing calls at home to change course and take a tougher line against North Korea, even from his core support base of young liberals, according to hundreds of comments posted online.

Moon, who swept to power after winning a May 9 election, remains hugely popular but his policy of pursuing both pressure and dialogue with the North is now under scrutiny.

Trump was blunt about the situation facing South Korea, one of Washington’s biggest allies in Asia.

“South Korea is finding, as I have told them, that their talk of appeasement with North Korea will not work, they (North Korea) only understand one thing,” he said in a tweet on Sunday, after the nuclear test.

Within South Korea, doubts about the “Moonshine” policy of engaging the North have been growing in recent weeks because there has been no change in the pace of the North’s ballistic missile testing since Moon took office.

The North twice test-fired intercontinental ballistic missiles in July. Now, despite international warnings, it conducted its sixth and most powerful nuclear test on Sunday.

“You said you will not have dialogue with the North if the North conducts a nuclear test. Keep your word,” said a post on the Facebook page of the presidential Blue House from a user named Kim Bojoong.

Moon said during his campaign for the presidency that dialogue would be “impossible for quite some time” if the North were to go ahead with another nuclear test.

However, Moon indicated on Sunday at a National Security Council meeting that he had not given up on using pressure to bring the North to the negotiating table, a sentiment he repeated on Monday in a telephone call with Japan’s Prime Minister Shinzo Abe.

“Pressure must be strengthened until the North comes to the table for dialogue,” the presidential Blue House quoted Moon as telling Abe.

Moon and Trump spoke by phone later on Monday, and the Blue House said the two agreed it was time to apply the strongest sanctions and pressure on North Korea and that stronger sanctions would be pursued at the United Nations.

“RATHER FEEBLE”

In another post on the palace’s Facebook page, user Shin Sanggyun said: “We know things are tough for you, mister president, but our response to the North’s nuclear pursuit has been rather feeble.”

It is time South Korea start considering using its shipbuilding expertise to build nuclear submarines and junior aircraft carriers, Shin said.

The Facebook posts were among hundreds of similar messages left on official social media maintained and monitored by the Blue House including its Twitter account and on the country’s largest Naver.com web portal.

Sentiment expressed on South Korea’s social media, where users are predominantly people in their 20s and 30s, has been a barometer of political support for Moon, a former human rights lawyer swept to power by an anti-graft movement that brought down his predecessor Park Geun-hye.

Moon’s support rating has slipped slightly in recent days but he remains hugely popular.

A public opinion survey by the Realmeter polling agency conducted two days before Sunday’s nuclear test and released on Monday showed support for Moon fell by 0.8 percentage point from a week ago to 73.1 percent.

But support among youngsters was strong with Moon getting an 85 percent approval rating among people in their 20s.

South Korea’s conservative opposition parties said the Moon government’s expectations about North Korea were unrealistic and isolating the country from its allies.

“While the Moon Jae-in government made appeasement gestures and haggled for dialogue despite the North’s continued provocations, we have become a nuclear hostage,” a senior Liberal Korea Party member, Kim Tae-heum, said on Monday.

Moon’s push for dialogue was bound to hit a dead end because Pyongyang never really considered the South as a dialogue partner, said Kim Jun-seok, political diplomacy professor at Dongguk University in Seoul.

“They have to acknowledge us as a partner for talks, but all North Korea wants is to talk with the United States,” Kim said.