BURLINGTON, Vt. — A pastor from Virginia was convicted Tuesday of helping a woman flee the country three years ago, when she was on the brink of having to turn over custody of her young daughter to the woman who was once her partner in a Vermont civil union.

The jury issued its verdict against the Rev. Kenneth Miller after several hours of deliberations in the case, which has drawn broad attention because of the legal and religious questions it raised about same-sex unions and child custody and because the whereabouts of mother and daughter remain unknown.

Miller, 46, a Mennonite from Stuarts Draft, Va., was charged with aiding in international kidnapping for helping Lisa Miller and her daughter, ­Isabella, leave the country in September 2009, a month after a judge indicated he would turn custody of the girl over to Janet ­Jenkins of Fair Haven, Vt., if Miller continued to defy a series of visitation orders.

Kenneth and Lisa Miller are not related. Lisa and Isabella, now 10 years old, were last known to be in Nicaragua.

As the jury was deliberating, Jenkins filed a lawsuit against both Millers and other people associated with the case, seeking unspecified monetary damages.

Kenneth Miller showed no emotion as the verdict was read and will remain free pending sentencing, although he was ­ordered to surrender his passport. After the verdict, his supporters walked out of the ­Burlington courthouse, lined up across the street and began singing hymns.

‘‘I am willing to accept the consequences of my actions,’’ said Miller, who could spend three years in prison. ‘‘I am at peace with God. I am at peace with my conscience, and I give it over to God, and at the same time I respect the decision of the court.’’

He said an appeal would be up to his lawyers, who left the courthouse shortly after the verdict was read.

Jenkins was not in court at the time, but her attorney said she is pleased that Kenneth Miller was being held accountable.

‘‘She hopes that the verdict will send a message to those who continue to aid and abet Lisa Miller in Nicaragua,’’ said attorney Sarah Star. ‘‘Her greatest hope is that the government’s efforts will lead to ­Isabella’s safe return to Vermont.’’

During three days of testimony, prosecutors used cellphone records and sometimes-reluctant witnesses to lay out a broad network overseen by Kenneth Miller that helped Lisa and Isabella travel first to Canada and then Nicaragua.

Prosecutors said Kenneth Miller arranged for another person to drive the two from Virginia to Buffalo, N.Y., where they crossed into Canada and were picked up by an Ontario Mennonite who took them to an airport. After they arrived in Nicaragua, prosecutors said, the two were cared for by American Mennonites who felt they needed to protect Isabella from what they considered a sinful lesbian lifestyle.

The United States does not have an extradition treaty with Nicaragua. The country is not a signer of the 1980 Hague convention on international child abductions,designed to return children illegally taken from member countries.

Lisa Miller and Jenkins ­entered into a civil union in Vermont in 2000, shortly after the state became the first to ­legally recognize same-sex relationships. Miller conceived the child through artificial insemination; both acted as parents.

Lisa Miller later became an evangelical Christian and renounced her homosexuality. A child-custody case went to ­Vermont family court in 2004, after the couple dissolved the civil union.