Yes, as long as you meet the other requirements for coverage, discussed in more detail at our site's family/medical leave page. Under FMLA, temp/leased employees are considered to be jointly employed by the leasing firm and the recipient employer, and must be counted by both the leasing firm and the recipient employer in determining employee coverage and employer liability.
As the primary employer of the worker, the temp agency/leasing firm is responsible for giving required notice to the employees, providing FMLA leave, and maintaining health benefits. In addition, the temp/leasing agency is primarily responsible for restoring the employee to the same or an equivalent job.
However, the recipient employer is also responsible if it replaces the employee with another leased employee from the same leasing agency. The recipient employer is also prohibited from interfering with the temp/leased employee's rights under the act or retaliating against an employee for asserting those rights.