Civilian casualties rose too when a wedding convoy near the fighting hit a landmine, killing at least one person.
Meanwhile, in Turkey, hundreds of people spilled to the streets in several cities to protest against PKK fighters.
Almost 1,000 demonstrators carrying Turkish flags gathered in Istanbul's central Taksim area on Sunday, chanting slogans against Abdullah Ocalan, the jailed PKK leader.
A PKK official told Al Jazeera on Sunday that it attacked Turkish forces as they attempted to enter Iraq, though earlier the group claimed Turkish troops had already crossed the border.
"I think it is pretty difficult to say troops shouldn't [invade] when the Turkish soldiers are being killed, and their villages attacked"
Celtic, Karlstad, Sweden
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Separately, a PKK spokesman told The Associated Press that a group of fighters killed and captured a number of Turkish forces during clashes about 70km inside Turkish territory.
"The PKK fighters were in a defensive position when they killed and injured a number of Turkish soldiers and captured another number," the spokesman, Abdul-Rahman al-Chadarchi, said without elaborating.
But Recep Tayyip Erdogan, the Turkish prime minister, says he will not immediately send troops into Iraq. He has held crisis talks with senior officials.
And after speaking with Condoleezza Rice, the US secretary of state, Erdogan said Washington had called on Turkey not to take action for a few days.
He is hoping for swift steps from the US, which opposes any Turkish unilateral military action, while sticking to Turkey's tough stance.
Erdogan said: "When we see the necessities that our security forces put in front of us, we will not hesitate to take steps. When this happens, we are ready to do what is necessary."
Iraq is also calling for restraint. The country's parliament has voted unanimously to adopt a resolution rejecting the use of force by Turkey to settle the border crisis.
Jalal Talibani, the Iraqi president, who is a Kurd, ordered PKK fighters to stop their attacks or leave Iraq.
On Sunday, Abdullah Gul, Turkey's president, met Erdogan and several top army officers and cabinet ministers to discuss Ankara's response to the attack.
Following the meeting, a statement from the president's office said: "While respecting the territorial integrity of Iraq, Turkey will not shy away from paying whatever price is necessary to protect its rights, its laws, its indivisible unity and its citizens."
The US strongly condemned the latest violence in Turkey's southeast and pledged co-operation with Ankara against PKK rebels.
"These attacks are unacceptable and must stop now. Attacks from Iraqi territory need to be dealt with swiftly by the Iraqi government and Kurdish regional authorities," Gordon Johndroe, a spokesman for George Bush, the US president, said on Sunday.
|Barzani, left, says Kurds would defend |
themselves if Kurdistan is attacked [AFP]
Al Jazeera's Barnaby Phillips in Silopi, Turkey, said the situation along the border was more tense than ever.
"The question is whether Turkey's soldiers and politicians feel as though they have now been pushed too far and that they must cross into northern Iraq."
Also on Sunday, Nuri al-Maliki, the Iraqi prime minister, denounced the PKK attack as a "terrorist operation" in a written statement, but just hours before that, the Iraqi parliament backed a motion condemning Ankara's threat of incursions.
"Iraq's parliament unanimously votes to condemn the threat of using force to solve the dispute. It feels that the Turkish parliament's decision to use force does not boost bilateral relations," the motion said.
Iraqi Kurdish leaders said they would rebuff any attack on their territory.
Caught in the middle
Al Jazeera's Hoda Abdel-Hamid, reporting from northern Iraq, said: "The position in general in the Kurdish region is that they want to keep out of this fight.
"However, they do say if Turkey comes into northern Iraq ... they won't sit there idle watching Turkish tanks rolling through their streets and through their mountains."
Massoud Barzani, the Kurdish leader of the largely autonomous northern Iraq region, said: "We are not going to be caught up in the PKK and Turkish war, but if Kurdistan region is targeted, then we are going to defend our citizens."
Speaking after a meeting with Jalal Talabani, the Iraqi president, he ruled out handing over PKK leaders to Ankara.