SEOUL (Reuters) - The breakdown at last month’s U.S.-North Korea summit has left South Korean President Moon Jae-in with little room to maneuver and exacerbated divisions within his government over how to break the impasse, three sources familiar with the issue said.

FILE PHOTO: South Korean President Moon Jae-in and North Korean leader Kim Jong Un wave during a car parade in Pyongyang, North Korea, September 18, 2018. Pyeongyang Press Corps/Pool via REUTERS/File Photo

The weeks since the Hanoi summit have revealed how difficult it may now be for Moon to play his desired role as a mediator, as Pyongyang and Washington have hardened their stances, threatening to make his focus on engagement seem implausible.

Some U.S. officials were frustrated when Moon, during a call with President Donald Trump just a week before the summit, offered to “ease the burden” by reopening inter-Korean economic projects as a concession to the North, two sources with knowledge of the matter said.

At the time, negotiations over North Korea’s nuclear program were “hardly making progress,” one source said.

That offer also landed with a thud among some of Moon’s own administration, who said it made him appear desperate for North Korean sanctions relief.

“You don’t want to look desperate, especially when their talks are going nowhere and time is ticking,” said the source, who like the others spoke on anonymity because of the sensitivity of the topic.

Moon is eager to restart the joint projects, key to an initiative that he sees as a boost for a moribund economy and the worst job market in a decade.

WEEKS OF CONTROVERSY

Moon’s approval ratings have fallen to their lowest levels since taking office in May 2017, pollster Realmeter said on Monday, citing recent missile activity in North Korea and the stalemate in nuclear talks.

Since the summit, work at North Korea’s Sohae rocket test facility has been detected, while a senior Pyongyang official said last week that Kim may suspend talks with the United States and rethink its freeze on weapons tests.

Senior North Korean negotiators have not showed up for weekly talks with the South at their liaison office since the summit broke down, according to Seoul’s Unification Ministry. But there were “no problems” communicating with the North, a ministry spokesman said on Wednesday.

Meanwhile, a recent U.S. State Department human rights paper criticized Seoul for pressuring North Korean defectors not to denounce Pyongyang. A separate U.N. report noted Seoul’s failure to declare its transfer of petroleum products used in the North, and published a photo of Moon and Kim riding in an “illicitly obtained” limousine in Pyongyang.

This week, the debate over whether Moon is too committed to engagement with North Korea boiled over in a controversy about a Bloomberg news report that called him a “top spokesman” for Kim Jong Un last year.

Moon’s office faced criticism from foreign media associations after ruling party officials used the racially charged term “black-haired foreigner” to personally single out the author of the Bloomberg story - who is South Korean - for being “almost treasonous.”

After days of pressure, the party apologized on Tuesday for using “black-haired foreigner,” while Moon’s office said it would take action if the reporter were “under real threat.”

CHANGING ROLES

Moon has vowed to act as a mediator between Trump and Kim, but that plan is in doubt in the wake of the summit’s collapse.

There was criticism in Washington that Seoul might have over-sold Kim’s denuclearisation commitment and gone too far in pushing for sanctions relief, according to another source who recently met with U.S. officials and academics.

On the other side, North Korea’s vice foreign minister told a news conference in Pyongyang last week that South Korea is only “a player, not an arbiter” because it is a U.S. ally, according to the Associated Press.

U.S. officials have said no sanctions will be lifted in exchange for partial steps toward denuclearisation, rejecting the incremental approach Pyongyang has sought.

But a senior aide to Moon on Sunday called for a small, step-by-step deal as a “realistic alternative” that would at least move toward dismantling the North’s nuclear facilities in return for sanctions relief.

“We need to reconsider the all-or-nothing strategy,” the official told reporters on condition of anonymity.

A U.S. State Department representative said that the United States remains prepared for a “constructive negotiation” but that North Korea was not yet ready.

The three sources say U.S. officials still think Moon’s administration can play a role in resuming talks the North, but they want it to focus more on pushing North Korea to denuclearise rather than advocating for sanctions relief.

“They do think South Korea could be a catalyst that helps the negotiations go in the right direction, but in a way that brings Kim’s commitments that deserve U.S. rewards,” said Shin Beom-chul, a senior fellow at the Asan Institute for Policy Studies in Seoul.