President Volodymyr Zelensky warned last month the military wanted to mobilise up to half a million people to battle the 600,000 or so Russian soldiers deployed in Ukraine.
The bill, introduced by the government in December, would toughen penalties for draft dodgers and lower the age of military service from 27 to 25.
While it would also cut compulsory wartime service from an unlimited period to 36 months, the changes have been deeply divisive in a nation exhausted by fighting.
"Some provisions directly violate human rights, some are not optimally formulated," ruling party leader David Arakhamia said after a closed door meeting with Ukraine's military leaders.
"We understand the request of the military command and are ready to meet it. But not all the rules can be supported," he said, adding that the bill had been returned to the government.
"In short, there will be no developments under the law on mobilisation. Neither today nor tomorrow. Nor in the near future," said Yaroslav Zheleznyak, an opposition MP from the pro-EU liberal Holos party.
Ukraine's defence minister said in the evening that his team had "already prepared a new version of the draft law" taking into account suggestions form other MPs.
The bill will be submitted for government approval and sent back to Parliament "in the near future", he said on Facebook.
"The mobilisation, military registration, and rotations, which are critically important for the state, are being politicised and stalled. This is unacceptable in wartime," he added.
During a press conference in Estonia on Thursday, Zelensky had acknowledged that military-aged Ukrainian men had illegally left the country to evade army service.
"If they are of mobilisation age, then they should help Ukraine. And they should be in Ukraine," he said during a press conference in Tallinn.
Ukraine, which counts roughly 850,000 soldiers among its ranks, has been trying to boost its numbers as Moscow ramps up pressure and deployments on the frontlines.
Kyiv does not disclose its losses, but after almost two years of trench warfare and a flagging counteroffensive, independent estimates put the figure in the tens of thousands.
bur-brw/PVH
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