SANAA, Feb. 11 (Xinhua) -- The UN Special Envoy to Yemen Martin Griffiths arrived in Yemen's rebel-held capital Sanaa on Monday to push for peace in the war-torn country.

This was Griffiths' fourth trip to Sanaa in fewer than two months in his attempts to push forward the implementation of Stockholm Agreement focusing on Yemen's Red sea port city of Hodeidah, the lifeline of Yemen's most commercial imports and humanitarian aid.

Meanwhile, Michael Anker Lollesgaard, head of the UN cease-fire monitor team, also arrived in Sanaa from the government-controlled southern port city of Aden to join Griffiths in his talks with the rebels.

The Stockholm Agreement calls for the prisoner exchange between the Yemeni government and Houthi rebels, a cease-fire and demilitarized zone in Hodeidah and the formation of a committee over the city of Taiz.

The cease-fire deal went into force on Dec. 18, 2018. However, both rival forces have blamed each other for violating the cease-fire.

The UN has said the discussions have been stalled because of different interpretations of the Stockholm Agreement over which side would control key points of Hodeidah during a partial cease-fire.

Lollesgaard, who chair a team of representatives from both the government and Houthis in Hodeidah, tabled last week a new plan for the withdrawal of rival forces from the port city and its surrounding positions, according to a UN statement.

The government representatives agreed to Lollesgaard's plan but Houthi rejected part of it, according to both government and Houthi media outlets.

Over the prisoner swap deal being negotiated in Jordan's capital Amman, the government side presses for the release of all war prisoners, while the Houthis want the release to be implemented in stages.

Saudi Arabia has been leading an Arab military coalition that intervened in Yemen in 2015 to support the government of President Abd-Rabbu Mansour Hadi after the Houthi rebels forced him into exile and seized much of the country's north, including Sanaa and Hodeidah.

The four-year war has killed more than 10,000 people, mostly civilians, displaced 3 million others and pushed the country to the brink of famine, according to the UN aid agencies.