The UK legislation was drawn up by the government to close a recently exposed loophole in the current law, which ministers fear could be used to justify unlicensed cloning experiments.
The bill is due to finish all stages in the Commons by the end of the week.
Danger to humans
Leading scientist and Labour peer Lord Winston, who is licensed to carry out research by the Human Fertilisation and Embryology Authority, gave his "wholehearted" backing to the proposed legislation.
Reproductive cloning was wrong, said Lord Winston, "firstly because it treats human beings like a commodity and that is dangerous and unacceptable.
"Secondly, because it carries very severe risks to the individual who is cloned at the present time."
Cloning of animals frequently produced abnormal results and this should not be allowed to happen to humans, Lord Winston said.
Responsible research
But he urged peers not to stand in the way of responsible embryo research, saying knowledge for good purposes gained in an ethically justified way was vital.
Lord Winston also urged caution about accepting the US "breakthrough" at face value, as it had yet to be properly reviewed by the scientific community.
The government action was prompted when anti-abortion campaigners, the Pro-Life Alliance, won a High Court ruling that laid bare a major deficiency in the legislation covering embryology research.
This flaw centred on the legal definition of an embryo - the union of an egg and a sperm.
Because a clone is produced in a different way, the judge ruled that current regulations did not embrace the new technology.
Maverick scientists
Maverick scientists, including Italian fertility doctor Severino Antinori, claimed the ruling meant they could make embryo clones in Britain and have them implanted before the emergency legislation could be brought in.
Health Minister Lord Hunt told peers the government would usually wait until the final outcome of the legal process, but he said the US developments showed these were not normal circumstances.
"The prospects of leaving unregulated in the light of the judgment the safety and ethical issues involved in bringing into the world artificially, a cloned child, are too much."
The government's critics say the country's embryology legislation is deeply flawed and there is little point in merely trying to patch it up.
Pro-life groups want both reproductive and therapeutic cloning banned.
Both the Conservatives and Liberal Democrats are backing the bill but worry about some of the details.
Lib Dem spokeswoman Baroness Sharp of Guildford complained about the speed at which it was being rushed through but supported it as a "stop-gap measure".
Tory spokesman Earl Howe also worried the bill might be deficient but said there was a "duty" to support its aims.