Mr Wheeler, a Democrat, said city workers would also be barred from travelling from Portland to Texas if councillors pass an emergency resolution during the session this week.
“The Portland City Council stands unified in its belief that all people should have the right to choose if and when they carry a pregnancy and that the decisions they make are complex, difficult, and unique to their circumstances,” Mr Wheeler’s office said in a statement.
Democrats in the city of Portland are considering a ban on trade and travel with Texas after Republicans in the southern US state introduced a widely criticised anti-abortion bill last week.
Councillors in the city will consider banning trading with Texas on Wednesday, Mayor Ted Wheeler announced on Friday.
The rebuttal follows the banning of abortions for women in Texas after six weeks through legislation informally known as the “heartbeat bill”.
He added that the resolution would remain in place until Texas Republicans withdraw the law, or if it gets overturned in court. But so far, the US Supreme Court has only issued a ruling allowing the “heartbeat bill” to be introduced.
Campaigners believe that a final decision from the court could still overturn it, despite justices leaning Republican. Many activists and Democrats – including Mr Wheeler – last week condemned the court for threatening to undo the abortion rights guaranteed in Roe v Wade, which legalised abortions in the US in 1973.
“We stand with Chief Justice John Roberts, Justice Elena Kagan, Justice Stephen Breyer, and Justice Sonia Sotomayor, who fought to block this attack on the reproductive rights, freedom, and autonomy of people across the country,” Portland’s mayor said of the four justices who ruled against the Texas bill.
“We urge other leaders and elected bodies around the nation to join us in condemning the actions of the Texas state government,” he continued.
“Portland City Council stands with the people who may one day face difficult decisions about pregnancy, and we respect their right to make the best decision for themselves.”
As well as banning abortions at around the six week mark, or when a heartbeat is detectable, the Texas legislation is unusual in that it allows anybody to file lawsuits against those accused of breaking it.