General Zinni: The US says setting up military bases was not the purpose of his visit
The Yemen news agency says the talks, which took place in Yemen, focused on the prospects for co-operation in defence and on the Middle East peace process.
The American Defence Secretary, William Cohen, said on Sunday that Washington planned to reduce its forces in the Gulf, following the end of the recent crisis with Iraq, but would retain the ability to rebuild them within two days.
Correspondents say the General's visit has prompted speculation that Washington may be seeking new military bases in Yemen.
Eight years ago the Yemeni government backed Iraq in the crisis over its invasion of Kuwait, but the American embassy in Yemen says the country's economic reform programme and moves towards greater democracy have since led to increasing co-operation.
Although this includes political and economic matters, it is the field of military co-operation that is attracting the most attention.
Although the US embassy in Yemen vigorously denies the suggestion that setting up military bases is on General Zinni's agenda, other western diplomats believe the idea has some foundation.
A diplomatic source in the Yemeni capital Sana'a told the BBC that fuel storage facilities for US warships in Aden is likely to be on the agenda in US-Yemeni talks.
Both diplomats and Yemeni journalists also believe that despite the denials, the US is interested in acquiring a base on Yemen's remote Indian Ocean island of Socotra.
US troops aiding Yemen
A small number of US troops are already in Yemen as part of a humanitarian aid programme to clear unexploded mines from the south of the country. US warships have been docking at Yemeni ports, and there are plans for new joint US-Yemeni training exercises.
General Zinni is the most senior military visitor to Yemen since the Gulf War. The last commander-in-chief of the US Central Command to pay a visit to Yemen was General Norman Schwarzkopf in 1989.
A year later, Yemen gave its support to Iraq's invasion of Kuwait, and US-Yemeni relations reached an all-time low.