Heavy fighting between government troops and opposition forces in various parts of Yemen has left 51 dead, according to military officials.

They said on Wednesday that forces loyal to President Abd-Rabbu Mansour Hadi had been engaged in combat with the Iran-allied Houthis and their allies in the Arabian Peninsula nation's northwest, near the border with Saudi Arabia, since Tuesday.

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.

Yemen's ongoing war keeps children out of school

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.

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

The United Nations says that 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.

John Kerry, the US secretary of state, said on Tuesday that the fighters were ready to observe a ceasefire plan taking effect this week, but the government swiftly dismissed the proposal.

Kerry spoke a day after meeting Houthi negotiators in Oman, but Hadi's government said it was not aware of any new peace initiative.

READ MORE: Kerry announces Yemen truce, FM says 'not interested'

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.

It was designed to allow aid deliveries to millions of Yemenis who are in need.

Against this backdrop of continued conflict, Human Rights Watch says that 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 more than 2,500 cases of detained and disappeared people. 

Source: AFP