BAGHDAD — Turkey’s prime minister visited Iraq yesterday and Kuwait promised to name its first ambassador in two decades, diplomatic victories for a fragile country that seeks fuller ties and clout with once-skeptical and suspicious neighbors.

Prime Minister Erdogan was the first Turkish leader to visit Iraq in nearly 20 years, and his Iraqi counterpart, Prime Minister al-Maliki, warmly greeted him at Baghdad’s airport. At a joint news conference, the two men agreed to pool their efforts to fight terrorism.

Turkey had expressed frustration over Iraq’s perceived reluctance or inability to hunt Kurdish rebels who conduct hit-and-run attacks on Turkish targets from bases in northern Iraq.

Backed by American intelligence, Turkey launched a cross-border ground offensive against the PKK rebel group in February. The brief campaign triggered protests from Iraq, although Mr. Erdogan said Iraq has cooperated with Turkish military operations on Iraqi soil and he expressed gratitude.

“The PKK is a terrorist organization, which is not only Turkey’s enemy but Iraq’s as well,” Mr. Erdogan said. “We will not allow such attempts to poison relations in the region or between the two countries.”

For his part, Mr. Maliki said he was pleased the leader of a strategic neighbor and regional economic power was in town.

Violence continues in Iraq, but Mr. Erdogan’s visit reflected a security situation that has improved more rapidly than many expected, partly because of the American troop surge in 2007 and new alliances between Sunni leaders and American forces.

Iraq is becoming increasingly bold in talks with Washington on an agreement that will govern the status of American troops in the country, and it now has time and confidence to reach out to other countries rather than lurch from one political and military crisis to the next.

“The Iraq of today is a constitutional Iraq that is searching for cooperation with the regional countries,” Mr. Maliki said.

He said Iraq and Turkey had agreed their prime ministers would meet at least once a year, and he welcomed Mr. Erdogan’s pledge to increase bilateral trade to $25 billion in the next 3-4 years.

The looming Kuwait move was also significant.

The Kuwait News Agency quoted the undersecretary of the Foreign Ministry, Khaled al-Jarrallah, as saying Kuwait would soon name a new ambassador to Iraq because of improved security.

Jordan and the United Arab Emirates have both named ambassadors in recent weeks, and Bahrain has said it’s in the process of doing so. Kuwait is considered particularly significant, although it is small and less influential, because it has not had an ambassador to Iraq since Saddam Hussein’s invasion of the country in 1990.