The rebel demand, made after the EU officially branded the Tigers a terrorist group, would force out 37 of the 57 monitors now in Sri Lanka to observe the country's increasingly shaky ceasefire signed in 2002.
In a statement the Sri Lankan government urged the Swedish-led mission, known by its acronym SLMM, to continue operations.
"The government of Sri Lanka urges the SLMM to continue to carry out its mandate despite the unreasonable stance of the LTTE (Liberation Tigers of Tamil Eelam)," the statement said.
"The time period of one month insisted on by the LTTE for effecting changes in the composition of the SLMM is tantamount to the imposition of a hostile deadline by the LTTE," it said.
The LTTE told peace broker Norway Wednesday that it did not want monitors from EU members Denmark, Finland and Sweden.
The diplomatic bickering comes amid a growing threat of renewed war on the embattled island, where more than 60,000 people have died in the Tamil separatist conflict since 1972.