NAIROBI, April 4  - A worldwide rig shortage is delaying oil drilling in east Africa, which is slowing growth and pushing up costs in one of the industry’s hottest new exploration areas, industry players and officials said.Companies exploring for oil and gas reserves in east Africa said they have had to queue up to secure a rig and pay top dollar when those rigs are procured.Last week British firm Tullow Oil Plc and its partner Africa Oil Corp. announced they had discovered oil in Kenya for the first time, while additional quantities of gas deposits have been discovered in neighbouring Tanzania and nearby Mozambique.Discoveries in east Africa and other new exploration areas have made demand particularly tight, said Terry Bonno, vice president of marketing at the world’s largest offshore drilling company, Transocean. "The availability of ultra-deepwater rigs for 2012 is very constrained,” Bonno said in a recent statement, emailed to Reuters in response to questions.The wait for a rig can last more than a year, and the rental price per day is often close to $500,000, according to analysts."Limited availability ... is pushing rates up quickly, as evidenced by a few fixtures for short-term programmes above the $600,000 a day level,” said Bonno, whose company has one ship off the coast of Mozambique. The average price for offshore rigs that drill deeper than 4,000 metres is about $450,000 per day, data firm RigZone says.Bonno said the shortage has been caused in part by a drilling boom and a slowdown in production of new drillships as a result of the economic recession in late 2008.This year the industry plans to build more than 50 new rigs, but Bonno expected the problem would persist for some time and would continue to push up the price of contracts. While rig shortages are global and have existed for many years, the outlook tends to be worse in areas with nascent oil and gas exploration, such as east Africa."Demand for deepwater rigs has gone up for use in east Africa ... there is definitely more international interest in the region,” Marne Beukes, an analyst who studies sub-Saharan Africa for global data firm IHS, said. "In the long-term it could get more difficult to secure a rig.” Among other complications associated with getting rigs in new areas, fewer rigs are under contract in the vicinity, which means that ships must travel longer, lesser known routes to reach new exploration projects.Kenya’s energy ministry said companies will need as many as half a dozen rigs in the coming year. Other east African countries also have busy drilling schedules; Tullow has said it plans to drill as many as 20 wells in Uganda next year.