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 with 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 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 (62 miles) away.
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 to 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.
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.