The continuing slump in global oil prices is punching holes in the budgets of oil-producing countries, including some OPEC members such as Iraq and Libya that are struggling with severe political and security problems.

Many members of the Organization of the Petroleum Exporting Countries need oil prices to average way above the current Brent crude oil price of $90 a barrel to balance their books. They have ratcheted up annual spending since the Arab Spring in 2011—and rely heavily on oil-export receipts for income.

But most Gulf monarchies with relatively small populations, such as OPEC’s biggest producer, Saudi Arabia, can cope with lower oil prices for some time, making it less urgent for them to cut output to boost prices.

Saudi Arabia said Friday it had increased crude output by 107,000 barrels a day in September to 9.7 million barrels daily. OPEC in total increased output last month to its highest level in more than a year.

That means the current price war within OPEC is set to continue, putting further pressure on weaker nations.

This week, Iran cut the price at which it sells light crude oil to Asia to its lowest level since December 2008, far below the $140 a barrel that analysts say it needs to balance its budget. The country is already subject to stifling international sanctions that have led to a protracted economic contraction.

“While Saudi Arabia, Kuwait and the United Arab Emirates could withstand a…drop in oil prices, many OPEC members will likely feel financial strain, making it hard to come to a consensus,” Morgan Stanley

Concern is rising fast in Iraq, where pressure to spend more on security is intense amid the advance of radical Islamic State fighters. It needs oil prices at around $106 a barrel to avoid an annual budget deficit, the International Monetary Fund estimates, a break-even level already 12% higher than in 2011.

“Our budget 95% depends on oil, so if there’s any decrease in the price, sure, it will negatively affect our budget,” said Najeeba Najeeb, a lawmaker with the Kurdistan Democratic Party. An Iraqi government spokesman didn’t respond to a request to comment.

Libya’s government estimates its budget may have to assume a sharp fall in oil prices, meaning pressure to cut outlays is getting higher, according to a government official. But as it battles rebels often aligned with al Qaeda and Islamic State, spending on “security and military defense is paramount,” said Salah al-Suhbi, a Libyan parliament member.

Algeria raised its welfare spending after neighbors Libya and Tunisia toppled their leaders in 2011. But it now needs oil prices at $121 a barrel to avoid a budget deficit, the IMF estimates, and could slip into the red in 2014 for the first time in 15 years. Algeria’s finance ministry declined to comment.

Struggling OPEC members are suffering partly for failing to diversify their economies when oil prices were high, analysts say. They also haven’t invested enough in their oil industries to sustain them through leaner times.

Countries faced with mounting deficits will now “hardly be able to fund their share of [exploration and production] investment” said Ali Aissaoui, a consultant at Arab Petroleum Investments Corp., a bank owned by Arab oil producers.

Nor will tapping international debt markets be easy. Major ratings firms don’t even assign credit ratings to Iraq and Libya. They rate the debt of fellow OPEC members Angola and Nigeria as speculative, making funding very expensive. The cost of servicing Nigerian debt has doubled in four years, according to its Debt Management Office.

Even Saudi Arabia’s finances are getting tighter. It needs oil to average $93 per barrel to stay in the black, Deutsche Bank

But with gross government debt at only 2.7% of gross domestic product in 2013, according to the IMF, the kingdom can suffer budget pain much more easily than its OPEC peers.

Write to Summer Said at summer.said@wsj.com and Sarah Kent at sarah.kent@wsj.com