The four tourists, all men, were abducted on Sunday by members of the al-Abdullah tribe as they were heading to the southern port city of Aden.
The tribesmen want some of their imprisoned relatives released, according to government officials.
“Meditation efforts are continuing and we are awaiting results,” General Rashad al-Alimi, the interior minister, told AFP news agency but he added that the negotiations were “yet to bear fruit”.
A French diplomat said that “the tone is optimistic” and Yemeni authorities believed that the hostages could be released in “a matter of hours”.
But earlier Mohammed al-Qibsi, an official in Shabwa province and one of the chief negotiators, told Associated Press that negotiations with the kidnappers had collapsed.
Officials said military action was being considered to secure the tourists’ release.
“At least 12 military vehicles are on their way to arrest the kidnappers and to free the four tourists,” said Naser al-Khudur, deputy governor of the province of Shabwa, told Reuters.
The four Frenchmen were in a convoy of foreign tourists when armed gunmen blocked the vehicle they were in and took them hostage.
The kidnapping in Shabwa province was the latest in a series of abductions of foreigners by armed tribesmen that have embarrassed the Yemeni government.
A French envoy based in the capital Sanaa said one of the hostages called Yemeni authorities shortly after the abduction and informed them that the hostages were being treated well and were healthy.
Elderly tribesmen began mediation efforts with the kidnappers, who are demanding the release of at least four fellow tribesmen jailed by the government for more than six months.
Ali Abdullah Saleh, the Yemeni president who is seeking re-election, has pledged to crack down on kidnapping, a tactic tribesmen frequently employ to win concessions from the government.
State control is shaky in rural areas of Yemen, a poor, mountainous nation on the southern tip of the Arabian peninsula.
According to Yemeni officials and media reports, as many as 325 people were kidnapped between 1991 and 2001. They include 91 French, 80 Germans, 37 Britons, 23 Americans and 22 Dutch.