diff --git a/core/repository/sparql/src/main/java/org/eclipse/rdf4j/repository/sparql/federation/RepositoryFederatedService.java b/core/repository/sparql/src/main/java/org/eclipse/rdf4j/repository/sparql/federation/RepositoryFederatedService.java
index 936733bfa58..9c8e7a47e7e 100644
--- a/core/repository/sparql/src/main/java/org/eclipse/rdf4j/repository/sparql/federation/RepositoryFederatedService.java
+++ b/core/repository/sparql/src/main/java/org/eclipse/rdf4j/repository/sparql/federation/RepositoryFederatedService.java
@@ -16,6 +16,9 @@
 import java.util.LinkedList;
 import java.util.List;
 import java.util.Set;
+import java.util.concurrent.ExecutorService;
+import java.util.concurrent.Executors;
+import java.util.concurrent.Future;
 
 import org.eclipse.rdf4j.common.iteration.CloseableIteration;
 import org.eclipse.rdf4j.common.iteration.EmptyIteration;
@@ -62,6 +65,10 @@ private class BatchingServiceIteration extends JoinExecutorBase<BindingSet> {
 
 		private final Service service;
 
+		private final ExecutorService threadExecutor = Executors.newSingleThreadExecutor();
+
+		private final Future<?> querySubmissionTask;
+
 		/**
 		 * @param inputBindings
 		 * @throws QueryEvaluationException
@@ -71,13 +78,26 @@ public BatchingServiceIteration(CloseableIteration<BindingSet> inputBindings,
 			super(inputBindings, null, EmptyBindingSet.getInstance());
 			this.blockSize = blockSize;
 			this.service = service;
-			run();
+
+			// Set up a consumer task to send HTTP requests in parallel. This must be done in a
+			// separate thread, because submitting HTTP requests may block if the HTTP pool is full.
+			// In that case, we would enter a deadlock, with the main thread waiting for both the
+			// pool to yield, and the consumer of the bindings to read from the queue.
+			// See: https://github.com/eclipse-rdf4j/rdf4j/discussions/5120
+			// Test case: https://github.com/tkuhn/rdf4j-timeout-test
+			try {
+				querySubmissionTask = threadExecutor.submit(this::run);
+			} catch (Exception e) {
+				throw new QueryEvaluationException("Failed to start a thread for batched federated query submission",
+						e);
+			}
 		}
 
 		@Override
 		protected void handleBindings() throws Exception {
+			// Note: any exceptions here will be intercepted by the caller and tossed asynchronously
+			// via the rightQueue.
 			while (!isClosed() && leftIter.hasNext()) {
-
 				ArrayList<BindingSet> blockBindings = new ArrayList<>(blockSize);
 				for (int i = 0; i < blockSize; i++) {
 					if (!leftIter.hasNext()) {
@@ -87,9 +107,19 @@ protected void handleBindings() throws Exception {
 				}
 				CloseableIteration<BindingSet> materializedIter = new CollectionIteration<>(
 						blockBindings);
+				// evaluateInternal is BLOCKING if the HTTP pool is exhausted
 				addResult(evaluateInternal(service, materializedIter, service.getBaseURI()));
 			}
 		}
+
+		@Override
+		public void handleClose() throws QueryEvaluationException {
+			super.handleClose();
+			if (querySubmissionTask != null) {
+				querySubmissionTask.cancel(true);
+			}
+			threadExecutor.shutdownNow();
+		}
 	}
 
 	/**
@@ -631,4 +661,4 @@ private static void closeQuietly(RepositoryConnection conn) {
 			logger.debug("Details: ", t);
 		}
 	}
-}
+}
\ No newline at end of file