diff --git a/llvm/lib/AsmParser/LLParser.cpp b/llvm/lib/AsmParser/LLParser.cpp
--- a/llvm/lib/AsmParser/LLParser.cpp
+++ b/llvm/lib/AsmParser/LLParser.cpp
@@ -1469,8 +1469,13 @@
 }
 
 Value *LLParser::checkValidVariableType(LocTy Loc, const Twine &Name, Type *Ty,
-                                        Value *Val, bool /* IsCall */) {
-  if (Val->getType() == Ty)
+                                        Value *Val, bool IsCall) {
+  Type *ValTy = Val->getType();
+  if (ValTy == Ty)
+    return Val;
+  // For calls, we also allow opaque pointers.
+  if (IsCall && ValTy == PointerType::get(Ty->getContext(),
+                                          Ty->getPointerAddressSpace()))
     return Val;
   if (Ty->isLabelTy())
     error(Loc, "'" + Name + "' is not a basic block");
diff --git a/llvm/lib/Bitcode/Reader/BitcodeReader.cpp b/llvm/lib/Bitcode/Reader/BitcodeReader.cpp
--- a/llvm/lib/Bitcode/Reader/BitcodeReader.cpp
+++ b/llvm/lib/Bitcode/Reader/BitcodeReader.cpp
@@ -5266,7 +5266,7 @@
             cast<PointerType>(Callee->getType())->getElementType());
         if (!FTy)
           return error("Callee is not of pointer to function type");
-      } else if (cast<PointerType>(Callee->getType())->getElementType() != FTy)
+      } else if (!OpTy->isOpaqueOrPointeeTypeMatches(FTy))
         return error("Explicit call type does not match pointee type of "
                      "callee operand");
       if (Record.size() < FTy->getNumParams() + OpNum)
diff --git a/llvm/lib/Bitcode/Writer/ValueEnumerator.cpp b/llvm/lib/Bitcode/Writer/ValueEnumerator.cpp
--- a/llvm/lib/Bitcode/Writer/ValueEnumerator.cpp
+++ b/llvm/lib/Bitcode/Writer/ValueEnumerator.cpp
@@ -467,8 +467,10 @@
         if (auto *GEP = dyn_cast<GetElementPtrInst>(&I))
           EnumerateType(GEP->getSourceElementType());
         EnumerateType(I.getType());
-        if (const auto *Call = dyn_cast<CallBase>(&I))
+        if (const auto *Call = dyn_cast<CallBase>(&I)) {
           EnumerateAttributes(Call->getAttributes());
+          EnumerateType(Call->getFunctionType());
+        }
 
         // Enumerate metadata attached with this instruction.
         MDs.clear();
diff --git a/llvm/lib/IR/Verifier.cpp b/llvm/lib/IR/Verifier.cpp
--- a/llvm/lib/IR/Verifier.cpp
+++ b/llvm/lib/IR/Verifier.cpp
@@ -3124,10 +3124,7 @@
          "Called function must be a pointer!", Call);
   PointerType *FPTy = cast<PointerType>(Call.getCalledOperand()->getType());
 
-  Assert(FPTy->getElementType()->isFunctionTy(),
-         "Called function is not pointer to function type!", Call);
-
-  Assert(FPTy->getElementType() == Call.getFunctionType(),
+  Assert(FPTy->isOpaqueOrPointeeTypeMatches(Call.getFunctionType()),
          "Called function is not the same type as the call!", Call);
 
   FunctionType *FTy = Call.getFunctionType();
diff --git a/llvm/test/Assembler/opaque-ptr.ll b/llvm/test/Assembler/opaque-ptr.ll
--- a/llvm/test/Assembler/opaque-ptr.ll
+++ b/llvm/test/Assembler/opaque-ptr.ll
@@ -98,3 +98,19 @@
     %b = atomicrmw add ptr %a, i32 %i acquire
     ret void
 }
+
+; CHECK: define void @call(ptr %p)
+; CHECK:     call void %p()
+; CHECK:     ret void
+define void @call(ptr %p) {
+  call void %p()
+  ret void
+}
+
+; CHECK: define void @call_arg(ptr %p, i32 %a)
+; CHECK:     call void %p(i32 %a)
+; CHECK:     ret void
+define void @call_arg(ptr %p, i32 %a) {
+  call void %p(i32 %a)
+  ret void
+}