Griffiths – whose efforts at kickstarting peace talks collapsed in September – is again trying to get the Iran-aligned Huthi rebels and the Saudi-backed government to the negotiating table by the end of the year.
He is expected to meet Huthi officials in the capital Sanaa on Wednesday.
Both sides have in the past week expressed their support for the envoy and his mission to hold talks in Stockholm, but fierce clashes erupted in the Red Sea city of Hodeida late on Monday after a lull.
Military officials said the battles were the worst since loyalists halted an offensive last week, and were concentrated in the eastern part of the city where rebels fired artillery.
Pro-government forces struck back, supported by warplanes from the Saudi-led coalition which launched a dozen raids, the sources said.
According to Huthi-run media, clashes lasted up to four hours and resulted in fatalities.
The city was relatively calm on Tuesday morning, according to an AFP correspondent who spoke to residents by telephone from Khokha about 100 kilometres away.
Call for truce
On Monday, Britain presented to the UN Security Council a draft resolution urging an immediate truce in Hodeida, whose port serves as an entry point to nearly all imports and humanitarian aid to the impoverished country.
The draft, circulated by Britain to the 14 other council members and seen by AFP, sets a two-week deadline for the warring sides ro remove all barriers to humanitarian aid.
The proposed resolution would significantly ratchet up pressure on the Saudi-led coalition and the Huthis to seek a negotiated settlement in Yemen, where millions are on the brink of starvation.
It also calls for a large injection of foreign currency to support Yemen's collapsing currency and for salaries of civil servants, teachers, and health workers to be paid within a month.
Mohammed Ali al-Huthi, head of the Huthi rebels' Higher Revolutionary Committee and an influential political figure, tweeted on Monday that he wanted his group to announce “readiness to suspend and halt all military operations” and stop firing missiles on Saudi Arabia.
Riyadh also lent its support to new talks.
Saudi King Salman told the Shura Council, his country's top advisory body, that the kingdom backed a “political solution” and a “comprehensive national dialogue” in Yemen.
Multiple past attempts to hold negotiations between the government alliance and Huthis have failed.
Griffiths said on Monday he hoped the rivals would meet in Sweden “within the next few weeks”. No date has yet been set.
'Stop selling weapons'
The Huthis seized Sanaa in late 2014, when they also took control of Hodeida and its port.
A year later, Saudi Arabia and its allies intervened in the war to bolster Yemeni President Abedrabbo Mansour Hadi.
Both parties in the conflict stand accused of acts that could amount to war crimes.
Human Rights Watch on Tuesday called on France to address laws-of-war violations with the UAE – a key member of the Saudi-led coalition – during Crown Prince Mohammed bin Zayed al-Nahyan's visit to Paris on November 21st.
“If President (Emmanuel) Macron is truly concerned about the humanitarian crisis in Yemen, he should tell the crown prince that France will stop selling weapons to the UAE if there's a real risk of their unlawful use,” said Benedicte Jeannerod, HRW's director for France.
Although Western governments have condemned civilian deaths in Yemen, they remain political and military backers of Saudi Arabia, which is a regional ally and spends billions of dollars on arms from the United States, Britain and France.
Swedish military exports rose by 2 percent last year, totalling 11.3 billion kronor, of which exports to Saudi Arabia accounted for 7 million kronor and exports to the UAE 149 million kronor.
The World Health Organization says nearly 10,000 people – mostly civilians – have been killed in Yemen since the Saudi intervention in March 2015, but rights groups believe the toll may be five times higher.
The World Food Programme says up to 14 million Yemenis are at risk of starvation.
On Monday, Saudi Arabia and the United Arab Emirates announced they would each give $250 million in aid to the war-ravaged country to support more than 10 million people.