(CNN) An Iranian baby with a serious heart defect will soon get the medical attention she needs in the United States.

The girl and her family -- caught up in President Donald Trump's immigration ban -- have received an all-clear to enter the United States for critical surgery, officials at the Oregon Health & Science University's Doernbecher Children's Hospital said.

Fatemeh Reshad and her parents are expected to arrive in the United States in a few days, the Portland hospital said Saturday.

They initially had been scheduled to meet Sunday with doctors in Portland but had been barred from traveling from Tehran, Fatemeh's uncle, Samad Teghizadeh, told CNN.

Several congressional Democrats released a letter Friday evening asking Secretary of State Rex Tillerson to grant a waiver for the child and her parents.

The delay came after Trump's executive order put an abrupt stop on travel to the United States for citizens of seven Muslim-majority countries, including Iran. A federal judge on Friday temporarily stopped the order.

Family attorney Jennifer Morrissey told CNN, "The family decided that it would be best to have their daughter treated at OHSU Doernbecher Children's Hospital because of the hospital's pediatric cardiology expertise and family support in Portland."

The uncle, Teghizadeh, who has been an American citizen for seven years, lives in Portland with his parents -- Fatemeh's grandparents -- who also are US citizens.

"Everything is going great, and we are bringing her here to Portland," Teghizadeh told CNN.

Fatemeh's family is "overwhelmingly relieved and thrilled that the baby is coming for surgery," Morrissey said at a press conference at the Portland hospital Saturday.

Family initially denied US visas

Last month, Iranian doctors in Tehran told Fatemeh's family that the 4-month-old has structural abnormalities and two holes in her heart, but they lacked the resources to treat the infant.

Fatemeh and her parents boarded a flight to Dubai, United Arab Emirates, but they were rerouted back to Iran and told to reapply for a US visa in 90 days.

Teghizadeh worried his niece wouldn't make it until then.

Fatemeh Reshad, a 4-month-old girl from Iran, needs urgent heart surgery.

A call for help

State and federal officials intervened on behalf of the family, Amber Murray, a Washington-based immigration attorney working on the case, told CNN.

Attorneys contacted State Department officials to help the family obtain an emergency waiver to navigate around the ban.

"I find it deplorable that an infant, who was supposed to come to Oregon to receive much needed lifesaving care, was not able to access that care at Oregon Health Sciences University," Oregon Gov. Kate Brown said at a press conference Thursday.

The governor's office connected with the family to determine if medical help could be provided, Brown spokesman Bryan Hockaday told CNN.

Fatemeh's family contacted the office of Sen. Jeff Merkley, D-Oregon, for help.

Merkley took "interest in the case and assigned a case worker from his office to work as a facilitator between the family and immigration lawyers," the senator's communications director Sara Hottman told CNN on Thursday.

"He's involved and very personally interested in this issue, being very opposed to this ban as it's having potentially devastating effect on lives," Hottman said.

That leverage apparently included the letter to Tillerson, which Merkley's office sent with other congressional Democrats from the state.

"Whether Fatemeh and her family are allowed access to this urgent and necessary medical care in the United States will determine whether she lives or dies," they wrote.

The Democrats said granting the waiver would be "moral and humanitarian" as well as send a signal that "even in the face of highly strained diplomatic relations, the United States offers help to those suffering tragic circumstances."

The surgery

Doctors from around the country and from Canada and Germany responded to calls for help, Murray told CNN.

"She has a fairly complicated anatomy with a muscular VSD," Murray said, referring to a ventricular septal defect.

It's a common heart defect present at birth due to an abnormal connection between the ventricles or lower chambers of the heart, according to the Mayo Clinic.

Doctors are awaiting more of Fatemeh's medical records, but the initial diagnosis indicates she also has other heart complications, including an atrial septal defect -- a "hole" in the wall that separates the top two chambers of the heart.

Physicians in Tehran sent the results of Fatemeh's echocardiogram to doctors in Portland, who reviewed her case and said she needs to be operated on urgently.

Doctors at OHSU Doernbecher have agreed to waive their fees, and the hospital will ensure the majority of the surgery is covered, the hospital said.

"This is my home. We live here. My work and everything is in the US," said Teghizadeh, the child's uncle. "Believe me, if I didn't have a brother and sister in Iran, I wouldn't go there. This is our home."

He said he just wants his sister's baby to get the care she needs.