Prime Minister Yemen has reaffirmed his government's decision to reject a ceasefire offer by John Kerry, the US secretary of state, a day after heavy fighting between government troops and opposition forces in various parts of Yemen left 51 dead.

The Arab coalition and Houthi fighters agreed to a temporary cessation of hostilities starting on November 17.

Fighting in Taiz and its surroundings on Tuesday killed 39 people, including five civilians, 20 soldiers and 14 fighters, military officials also said.

The UN says more than 7,000 people have been killed and nearly 37,000 wounded in Yemen since the Arab coalition launched a military campaign in March 2015 in support of the internationally recognised Hadi government against the Houthis.

Millions are in need of food aid, and another 21 million people urgently need health services, according to the UN.

Six attempts to clinch a ceasefire in Yemen have failed so far, including a three-day October truce that fell apart as soon as it went into force.

Against this backdrop of continued conflict, Human Rights Watch says the Houthis and other authorities in Sanaa have "arbitrarily detained, tortured and forcibly disappeared" opponents.

The New York-based rights watchdog cited on Thursday two recent deaths in custody and 11 cases of torture, calling on authorities to take action.

It also said that a local rights organisation, Mwatana, was working on over 2,500 cases of detained and disappeared people. 

Shortly after the announcement, Abdel-Malek al-Mekhlafi, the foreign minister, said his government was not interested in the latest ceasefire plan involving the Houthis.

He repeated the government's stance on Thursday, saying there was no agreement but just "a declaration which means nothing".

"We have rejected the agreement because there is no agreement in principle," Mekhlafi told Al Jazeera.

"We have only a declaration that means nothing. It's an agreement between Kerry and the Houthis.

"We have our own reasons to refuse it because it doesn't commit to the international agreement and gives a lot of power to the Houthis, more than what the Yemeni people accept. Houthis are a minority in the country."

On Wednesday, forces loyal to President Abd-Rabbu Mansour Hadi engaged in combat with the Iran-allied Houthis and their allies in the Arabian Peninsula nation's northwest, near the border with Saudi Arabia.

The fighting came as loyalists launched an attack on three fronts to recapture the coastal town of Midi and nearby Haradh, the officials quoted by the AFP news agency said.

Fifteen loyalists and 23 fighters were killed in the clashes, they said.

"Our military operations will continue until we push them out," said army Colonel Abdul Ghani al-Shubaili, whose forces had air support from an Arab coalition assembled by Saudi Arabia that is backing Hadi.

Elsewhere, nine fighters and four soldiers were killed in fighting on the outskirts of the flashpoint city of Taiz, in southwest Yemen, military officials said.

Pro-Hadi forces have advanced towards the city's presidential residence and police headquarters, both under opposition control, witnesses said, reporting heavy fighting and loud explosions that shook the city.