The move means Congress has now approved an expenditure of more than $500 billion for the two conflicts.
About $23 billion of the fund is to replace and refurbish equipment worn out in the harsh environments of the wars.
However, the bill will bar the US administration from using the fund to build permanent military bases in Iraq or to exercise control over Iraq’s oil sector.
Democrats and many republicans say the Iraqi insurgency has been fuelled by perceptions that the US is aiming toward a permanent presence in the country.
They have called on Bush to make a policy statement that no such plans exist.
The Senate is expected to pass the final version of the bill, that approves a total expenditure of $447.6 billion, by this weekend before sending it to George Bush, US president, for signature.
The House passed the bill by 394-22 votes with virtually no debate as politicians aimed to complete business before a break to campaign for November congressional elections.
Lawmakers called the $70 billion a "bridge fund" to last halfway through the next fiscal year, beginning October 1.
The bill also provides $377.6 billion for the Pentagon's core programmes, $4.1 billion less than Bush wanted, but $19 billion above current levels, and also funds a military pay rise.