Labour planns to propose further restrictions on the sale of crossbows, days after a pregnant 35-year-old woman was shot and killed with one of the weapons at her home in east London.

The party is examining how it could amend the offensive weapons bill making its way through parliament to introduce further restrictions. Sale of crossbows is simply restricted for under-18s.

Labour wants to respond to the killing of Sana Muhammad in Ilford on Monday morning. She was shot with a crossbow in her family home and died shortly afterwards, but her baby son was delivered by caesarean and survived.

Earlier, Theresa May indicated at prime minister’s questions that the government would consider whether fresh restrictions were necessary. The PM told the Commons she would “consider the risk that such weapons pose to public safety and whether further measures are needed”.

May was responding to Muhammad’s MP, Wes Streeting, who said the killing “had shocked people up and down the country to the core”.

Streeting said weapons such as the crossbow that killed Muhammad were readily available for purchase online and asked the prime minister to consider toughening up “the scope of the laws governing the sale, possession and use of these deadly weapons”.

Unlike guns, crossbows are subject to limited regulation. The weapons are legal for anybody aged over 18 to buy and can easily be found online. They are not subject to licensing, and purchasers are not subject to additional checks as buyers of guns are, although possessing one in a public place may, in some circumstances, be an offence.

Labour sources told the Guardian that the party was working on a number of potential amendments to the bill. “The laws are clearly too lax; there isn’t, for instance, any specific licensing regime,” a source said.

Muhammad was eight months pregnant when she was shot with the weapon. A man, Ramanodge Unmathallegadoo, has been charged with her murder.

At the time her husband, Imtiaz Muhammad, told the Evening Standard: “The arrow went up into her heart but did not touch the unborn baby. The baby was due in four weeks. They operated with the arrow still in because it would have been too dangerous to take out.”

Streeting said he welcomed the prime minister’s commitment to look again at the case for further tightening the law.