Sleiman has said he will not sign any unjust law or one that does not further social justice.
The president’s signature is necessary for the law, which was recently endorsed by Parliament, to go into effect.
Longtime tenants have been holding protests urging Sleiman not to sign the rent law.
In turn, landlords have held several counterdemonstrations, urging the president to sign it.
Parliament passed dozens of draft bills in a series of sessions earlier this year. The president has signed all of the laws except the controversial draft rent bill. The other laws, which covered a range of topics from domestic violence to Civil Defense volunteers, will go into effect after they are published in the Official Gazette.
Tenants have said that the law would displace thousands of families who rent in Beirut under an old law that governs lease contracts enacted before 1993.
Inhabitants pay minimal rent fees that often amount to less than LL1,000,000 annually. Under the new law, rents would increase over six years until they reach 5 percent of the current market value of an apartment. Owners have the freedom to either sell the apartment or lease under a new contract and price.
Meanwhile, a group of landlords protested outside the National Musuem, asking Sleiman to sign the law, saying most of the owners were also part of the working class in the country and needed to be treated fairly.