April 8 (Reuters) - The interest rate on the most popular U.S. home loan ticked down last week for the first time since the start of the Iran war, but not enough to rejuvenate a housing market that's pricing out many buyers with a combination of elevated borrowing costs and expensive homes.

The Mortgage Bankers Association said on Wednesday the contract rate on a 30-year, fixed-rate mortgage fell 6 basis points to 6.51% for the week ended April 3, retreating from the seven-month high hit the prior week.

Even so, refinance applications sank 2.8%, and purchase applications, while up about 1% from the previous week, were 7% lower than a year ago, the MBA said. 

Mortgage rates have climbed by 42 basis points since the United States and Israel launched the war on February 28, driving up yields on the Treasury bonds lenders use to set mortgage rates. 

Besides raising the cost of loans, the Iran war has also hit consumers' daily budgets with the surge in fuel prices. 

Housing affordability has been a key political issue for the Trump Administration, which is readying what it says will be a "major housing announcement" on Wednesday.

Earlier this year President Donald Trump proposed banning institutional investors from buying single-family homes and told Fannie Mae and Freddie Mac - the government-controlled entities that back the majority of U.S. home loans - to purchase $200 billion in mortgage-backed securities to push down borrowing rates.