In a news conference after al-Jaafari met the Turkish Prime Minister Recep Tayyip Erdogan on Friday, Erdogan stressed his country's support of Iraq's territorial integrity.
"Iraq's stability is vital to Turkey's stability," Erdogan said.
"Turkey is prepared to train Iraqi security troops, and we hope that Iraq would overcome its current security difficulties," he added.
Al-Jaafari - on his first official trip abroad since taking over as the prime minister - and Erdogan met in Ankara to discuss economic and security issues between the two neighbours.
"Iraq needs Turkey's support during the current exceptional circumstances," al-Jaafari said.
"We seek to develop Iraq's relations with Turkey and other neighbouring countries."
"Iraq needs Turkey's support during the current exceptional circumstances"
Iraqi prime minister
But al-Jaafari added that even though his country wants to strengthen ties with all countries, Iraq "will never accept anything from any country that would harm us and especially it is out of the question for us to accept something that is harming our security and economy".
Al-Jaafari also announced on Friday that he would soon visit neighbouring Syria to demand a crackdown against foreign fighters crossing into Iraq.
Al-Jaafari, who gave no further details of the visit, said Iraq would not tolerate foreign fighters crossing the desert between the two countries.
"There are some armed groups infiltrating from Syria... How much of this infiltration is related to the Syrian government, we will discuss this issue directly with Syrian authorities," al-Jaafari said.
"We will visit Syria some time soon, and one of the issues that will be taken up will be the security file and the prevention of such infiltrations," he said.
Al-Jaafari (C) is planning to visit
Syria to discuss border security
Iraq and the United States have been increasing pressure on Syria to do more to halt cross-border infiltrations amid growing violence that has left more than 520 people dead since the new Iraqi government was announced on 28 April.
Al-Jaafari, who arrived in Turkey aboard Erdogan's official plane, is accompanied by a large government delegation that includes the ministers of oil, finance, trade, electricity and industry. The minister for water resources is expected to join the delegation on Saturday, the Turkish Anatolia news agency said.
The Turkish paper The Daily Hurriyet reported on Wednesday that tough bargaining was expected over an outstanding $1.7 billion of Iraqi debt to Turkish firms, mostly for fuel provided since the March 2003 US-led invasion of Iraq.
Turkey wants to help rebuild the war-torn country and supports the postwar political process, but has several concerns that it sees directly linked to its own security.
Ankara is frustrated that no action has been taken against an estimated 5000 rebels of the outlawed Kurdistan Workers Party (PKK), considered terrorists by both Turkey and the United States, since October 2003, when the two sides agreed on an action plan that included military options.
At a three-way meeting in January, Iraqi, US and Turkish officials discussed measures to tackle the rebels, including intelligence cooperation, but the talks failed to produce any immediate military action.
Turkey is frustrated no action
has been taken against the PKK
Turkey was expected to ask al-Jaafari to act on a list of wanted PKK fighters that it has handed both to Baghdad and the US forces in Iraq, according to Osman Korutuk, Turkey's top diplomat dealing with Iraq.
"We waited for the (Iraqi) government to come into office for any action to be taken regarding the list. Now we expect the government to determine the whereabouts of these people, arrest and extradite them," he told the NTV news channel on Wednesday.
Another worry for Turkey is the future of the oil-rich city of Kirkuk, claimed by Iraqi Kurds as well as Turkmen - an Iraqi minority of Turkish descent.
Turkey suspects Iraqi Kurds of plotting to break away from Baghdad and make Kirkuk the capital of a future independent state - a nightmare scenario for Ankara, which fears possible fallout on its own sizeable Kurdish community.
Al-Jaafari will meet Turkish parliament speaker Bulent Arinc on Saturday before flying back home.