The owner of the White Rose Centre and Castleford's Xscape venue, said it has received £77 million in rent payments for the quarter to June 24.
The group said there is £18 million of rent outstanding, with £6 million of this relating to customers where concessions have been agreed but documentation is pending.
In May, the company reported that losses for the 12 months to March 31 widened sharply to £1.4 billion after it saw rental income plunge.
Landsec, which owns large areas of property in central London, said it has been encouraged by the recent loosening of pandemic restrictions.
Chief executive Mark Allan said: “As restrictions are reduced, we’re seeing more people returning to work and more businesses trading more freely.
“We’ve been delighted with the numbers of our customers and partners who have engaged with us as a result, both to address their rent arrears and pay a sustainable rent as they are trading again.”
Mr Allan said this shows that the Government’s broad approach to rolling back the current rent moratorium has brought “landlords and tenants together to negotiate constructively”.
The ban on commercial evictions had been due to expire in June until March next year.
But Mr Allan called on the Government to accelerate this to address tenants who will not negotiate.
“However, it also highlights the need to accelerate the moratorium legislation so that we can meaningfully address those last remaining well-capitalised businesses who continue to refuse to engage with us,” he said.
Shares in the company were 2.2% higher at 682.1p in early trading on Friday.