Iraqi PM promises to defend Kurds against any attack
"To our people in the Kurdistan region: we defend our Kurdish citizens as we defend all Iraqis and will not allow any attack on them," he tweeted in English.
An Abadi adviser, who asked to remain anonymous, told AFP that the premier was referring to either an internal or external attack.
"We will not allow any harm to you and we will share our loaf of bread together," Abadi said in another tweet.
Iran on Saturday said it would hold a joint military exercise with Iraq on Iran's border with Iraqi Kurdistan in response to Monday's "illegitimate referendum".
Iraqi soldiers on Tuesday also took part in a Turkish military drill close to the Iraqi frontier.
Inside Iraq, Hadi al-Ameri, head of the powerful Iran-backed Badr organisation, has vowed to defend the country's unity, warning that the poll could trigger civil war.
Baghdad has demanded the annulment of Monday's non-binding referendum, which resulted in a huge "yes" vote, and has suspended international flights to and from the region.
Washington has said it does not recognise the "unilateral" referendum.
Turkey, Iran and Syria - which have their own sizeable Kurdish communities - have also rejected the vote for independence in the oil-rich region.
On Saturday, Abadi explained Baghdad's wish to better control all of Iraq's oil revenues.
"Federal government control of oil revenues is in order to pay KR employee salaries in full and so that money will not go to the corrupt," he tweeted.
In 2014, after a dispute over oil exports, Baghdad suspended payments to the Kurdish region of 17 percent of Iraq's national budget.
Wages, including those of Kurdish Peshmerga fighters, were slashed after the end of those transfers, which were worth around $12 billion (10 billion euros) annually and made up 80 percent of the region's budget revenues.