The time had come for "calm reflection" as the law was "very complex", he said.
Alan and Judith Kilshaw, who paid £24,000 to adopt the six-month-old babies in the US, lost their fight to look after the girls while social services carry out a full investigation into the case.
Mr Justice Kirkwood, sitting at Birmingham Priory Courts on Tuesday, said the girls should remain in temporary foster care arranged by Flintshire County Council.
A later hearing will decide who should care for the children and whether they should be returned to the US.
'Time for calm reflection'
Mr Kirkwood told journalists waiting for the decision on Tuesday that the court was now in control of the case.
He said he had asked the official solicitor to investigate all the circumstances surrounding the case in the UK and in the US, where the twins were adopted.
The time had come for "calm reflection" as the law was "very complex", he said.
"It is not just English law that I have to consider, but the position also in one, two or perhaps three states of the United States of America," he said.
"I am sure that everybody understands that this court's task is to do its best to find the right solution for the twins.
"It's their welfare that really matters in all of this."
Public outcry
The legal process to determine who should have the twins permanently could include the birth-mother Tranda Wecker and an American couple who claim they were first to adopt the baby girls.
The girls were taken into temporary foster care after an emergency protection order was obtained by Flintshire social services last Thursday, following the outcry surrounding the case.
It is still unclear whether the Kilshaws will be allowed to visit the girls, named Belinda and Kimberley, in their foster home.
Mr Kirkwood said he hoped to have the whole case resolved within a few weeks.