MPs voted against the proposals to accept 3,000 children in a move similar to the kindertransport by 294 to 276.
But after criticism, the Prime Minister said he would accept the amendment now that it no longer included the figure of 3,000 children that it had originally asked for.
Lord Woolf said he hoped the fund and Initial offer of £100,000 would “demonstrate leadership and spur on others to make their own practical and financial contribution towards this effort.”
Before Lord Weidenfeld passed away last year he launched a rescue mission of up to 2,000 Christian families from Syria and Iraq.
Weidenfeld's Safe Havens Fund flew 150 Syrian Christians who were fleeing Daesh (sometimes known as Isis) to Warsaw on Friday to seek refuge in Poland.